UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM N-Q

             QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED
                         MANAGEMENT INVESTMENT COMPANIES

Investment Company Act file number 811-5707

                          Van Kampen High Income Trust
--------------------------------------------------------------------------------

               (Exact name of registrant as specified in charter)


              1221 Avenue of the Americas, New York, New York 10020
--------------------------------------------------------------------------------

               (Address of principal executive offices) (Zip code)


                                 Ronald Robison
              1221 Avenue of the Americas, New York, New York 10020
--------------------------------------------------------------------------------

                     (Name and address of agent for service)

Registrant's telephone number, including area code: 212-762-4000

Date of fiscal year end: 12/31

Date of reporting period: 3/31/05



Item 1.  Schedule of Investments.

The Trust's schedule of investments as of the close of the reporting period
prepared pursuant to Rule 12-12 of Regulation S-X is as follows:

       
 
VAN KAMPEN HIGH INCOME TRUST 

PORTFOLIO OF INVESTMENTS MARCH 31, 2005 (UNAUDITED)
                                                        
                                                                                                                        
                                                                                
PAR                                                                 
AMOUNT                                                              
(000)          DESCRIPTION                                             COUPON         MATURITY               VALUE  
                                                                                                 
                                                                    
               CORPORATE BONDS   167.2%                              
               AEROSPACE   1.3%                                      
$        675   K&F Acquisition, Inc., 144A - Private Placement (a)      7.750%        11/15/14             $   658,125
                                                                                                          -------------
                                                                    
               BROADCASTING   0.6%                                 
         295   Salem Communications Corp.                               7.750         12/15/10                 307,169
                                                                                                          -------------
                                                                    
               CABLE   10.3%                                       
         575   Cablevision Systems Corp., 144A - Private Placement                                
               (a) (b)                                                  6.669         04/01/09                 612,375
       1,005   Charter Communications Holdings LLC                      9.625         11/15/09                 791,437
         855   Echostar DBS Corp.                                       6.375         10/01/11                 842,175
       1,260   Intelsat Bermuda Ltd - 144A - Private Placement                                    
               (Bermuda) (a) (b)                                        7.805         01/15/12               1,285,200
          45   Intelsat Bermuda Ltd - 144A - Private Placement 
               (Bermuda) (a)                                            8.250         01/15/13                  45,675
         975   Kabel Deutschland GmbH, 144A - Private Placement
               (Germany) (a)                                           10.625         07/01/14               1,082,250
         400   PanAmSat Corp.                                           9.000         08/15/14                 424,000
                                                                                                          -------------
                                                                                                             5,083,112
                                                                                                          -------------
                                                                    
               CHEMICALS   13.4%                                   
         610   Equistar Chemicals LP                                   10.125         09/01/08                 677,100
         350   Equistar Chemicals LP                                   10.625         05/01/11                 394,625
         245   FMC Corp.                                               10.250         11/01/09                 274,400
         190   Huntsman Advanced Materials LLC, 144A - Private                                 
               Placement (a)                                           11.000         07/15/10                 218,975
         425   Innophos, Inc.,144A - Private Placement (a)              8.875         08/15/14                 448,375
         190   ISP Chemco, Inc.                                        10.250         07/01/11                 206,625
         900   ISP Holdings, Inc.                                      10.625         12/15/09                 967,500
         145   Koppers, Inc.                                            9.875         10/15/13                 162,400
         780   Lyondell Chemical Co.                                   10.500         06/01/13                 900,900
          55   Millennium America, Inc.                                 7.000         11/15/06                  56,100
         520   Millennium America, Inc.                                 9.250         06/15/08                 560,300
         535   Nalco Co.                                                7.750         11/15/11                 559,075
         495   Rhodia SA (France)                                       8.875         06/01/11                 483,862
         600   Rockwood Specialties Group, Inc.                        10.625         05/15/11                 669,000
                                                                                                          -------------
                                                                                                             6,579,237
                                                                                                          -------------





                                                                                               
               CONSUMER PRODUCTS   5.1%                                                 
         270   Amscan Holdings, Inc.                                    8.750         05/01/14                 263,250
         185   Del Laboratories, Inc., 144A - Private Placement (a)     8.000         02/01/12                 178,525
         210   Oxford Industrials, Inc.                                 8.875         06/01/11                 223,650
         875   Phillips Van-Heusen Corp.                                7.250         02/15/11                 892,500
         635   Rayovac Corp.                                            8.500         10/01/13                 657,225
         145   Rayovac Corp., 144A - Private Placement (a)              7.375         02/01/15                 139,562
         158   Tempur Pedic, Inc.                                      10.250         08/15/10                 178,145
                                                                                                          -------------
                                                                                                             2,532,857
                                                                                                          -------------
                                                                    
               DIVERSIFIED MEDIA   9.0%                                                 
         827   Advanstar Communications, Inc. (b)                      10.294         08/15/08                 860,496
         750   CanWest Media, Inc. (Canada)                            10.625         05/15/11                 821,250
         395   Dex Media West/Finance Corp., LLC                        9.875         08/15/13                 442,400
         655   Houghton Mifflin Co.                                     9.875         02/01/13                 677,925
         135   Interpublic Group of Cos, Inc.                           5.400         11/15/09                 129,937
         185   Interpublic Group of Cos, Inc.                           6.250         11/15/14                 175,750
         425   Marquee, Inc., 144A - Private Placement (a) (b)          7.044         08/15/10                 446,250
         860   Primedia, Inc.                                           8.875         05/15/11                 900,850
                                                                                                          -------------
                                                                                                             4,454,858
                                                                                                          -------------
                                                                    
               ENERGY   15.6%                                      
         455   CHC Helicopter Corp. (Canada)                            7.375         05/01/14                 445,331
         395   CHC Helicopter Corp., 144A - Private Placement 
               (Canada) (a)                                             7.375         05/01/14                 386,606
         285   CITGO Petroleum Corp.                                    6.000         10/15/11                 282,862
         905   El Paso Production Holding Co.                           7.750         06/01/13                 920,837
         860   Frontier Oil Corp.                                       6.625         10/01/11                 860,000
          90   Hanover Compressor Co.                                   8.625         12/15/10                  94,500
         385   Hanover Compressor Co.                                   9.000         06/01/14                 413,875
         375   Hanover Equipment Trust                                  8.500         09/01/08                 392,812
         160   Hanover Equipment Trust                                  8.750         09/01/11                 169,600
         550   Hilcorp Energy, Finance Corp., 144A - Private                                 
               Placement (a)                                           10.500         09/01/10                 613,250
         188   Magnum Hunter Resources, Inc.                            9.600         03/15/12                 211,500
         375   Pacific Energy Partners                                  7.125         06/15/14                 390,000
         850   Plains Exploration & Production Co.                      7.125         06/15/14                 892,500
         283   Port Arthur Finance Corp.                               12.500         01/15/09                 329,322
         180   Tesoro Petroleum Corp.                                   9.625         04/01/12                 198,450
       1,025   Vintage Petroleum, Inc.                                  7.875         05/15/11               1,091,625
                                                                                                          -------------
                                                                                                             7,693,070
                                                                                                          -------------
               FINANCIAL   1.5%                                    
         680   Refco Finance Holdings LLC, 144A - Private 
               Placement (a)                                            9.000         08/01/12                 724,200
                                                                                                          -------------
                                                                    
               FOOD & DRUG   4.9%                                  
         690   Delhaize America, Inc.                                   8.125         04/15/11                 770,399
         150   Jean Coutu Group (PJC), Inc. (Canada)                    7.625         08/01/12                 153,750
         885   Jean Coutu Group (PJC), Inc. (Canada)                    8.500         08/01/14                 863,981
       1,570   Jitney-Jungle Stores America, Inc. (c) (d) (e)          12.000         03/01/06                       0
         635   Rite Aid Corp.                                           8.125         05/01/10                 647,700
                                                                                                          -------------

                                                                                                             2,435,830
                                                                                                          -------------








                                                                                               
               FOOD & TOBACCO   8.0%
         750   Constellation Brands, Inc.                               8.000         02/15/08                 804,375
         340   Michael Foods, Inc.                                      8.000         11/15/13                 355,300
         210   Pilgrim's Pride Corp.                                    9.250         11/15/13                 232,050
         765   Pilgrim's Pride Corp.                                    9.625         09/15/11                 833,850
         380   Smithfield Foods, Inc.                                   7.000         08/01/11                 390,925
         220   Smithfield Foods, Inc.                                   7.625         02/15/08                 227,700
       1,050   Smithfield Foods, Inc.                                   8.000         10/15/09               1,118,250
                                                                                                          -------------
                                                                                                             3,962,450
                                                                                                          -------------
                                                                    
               FOREST PRODUCTS   8.5%                                                 
         510   Abitibi-Consolidated, Inc. (Canada)                      6.000         06/20/13                 443,700
         330   Abitibi-Consolidated, Inc. (Canada)                      8.550         08/01/10                 336,600
         535   Georgia-Pacific Corp.                                    8.875         02/01/10                 599,869
         775   Graphic Packaging International, Inc.                    9.500         08/15/13                 825,375
         560   MDP Acquisitions PLC (Ireland)                           9.625         10/01/12                 604,800
         495   Pliant Corp.                                            13.000         06/01/10                 420,750
       1,065   Tembec Industries, Inc. (Canada)                         7.750         03/15/12                 974,475
                                                                                                          -------------
                                                                                                             4,205,569
                                                                                                          -------------
                                                                    
               GAMING & LEISURE  12.5%                                                
         425   Ceasars Entertainment                                    8.875         09/15/08                 466,969
         920   Harrahs Operating Co., Inc.                              7.875         12/15/05                 940,700
          78   HMH Properties, Inc.                                     7.875         08/01/08                  79,950
         275   Host Marriott LP                                         7.125         11/01/13                 274,312
         550   Host Marriott LP, 144A - Private Placement (a)           6.375         03/15/15                 528,000
         625   Isle of Capri Casinos, Inc.                              7.000         03/01/14                 621,875
         150   MGM Mirage, Inc.                                         5.875         02/27/14                 142,312
       1,120   MGM Mirage, Inc.                                         6.000         10/01/09               1,110,200
         865   Mohegan Tribal Gaming Authority                          7.125         08/15/14                 871,487
         490   Park Place Entertainment Corp.                           7.875         12/15/05                 501,637
         625   Station Casinos, Inc.                                    6.000         04/01/12                 623,437
                                                                                                          -------------
                                                                                                             6,160,879
                                                                                                          -------------
                                                                    
               HEALTHCARE   10.2%                                  
         390   AmerisourceBergen Corp.                                  8.125         09/01/08                 420,225
         340   Community Health Systems, Inc., 144A - Private                 
               Placement (a)                                            6.500         12/15/12                 333,200
         230   DaVita, Inc., 144A - Private Placement (a)               6.625         03/15/13                 228,850
         115   DaVita, Inc., 144A - Private Placement (a)               7.250         03/15/15                 113,275
       1,140   Extendicare Health Services, Inc.                        6.875         05/01/14               1,131,450
         400   Fisher Scientific International, Inc.                    8.125         05/01/12                 436,000
         160   Fisher Scientific International, Inc., 144A - Private                                       
               Placement (a)                                            6.750         08/15/14                 163,200
          56   Fresenius Medical Care Capital Trust II                  7.875         02/01/08                 588,700
         235   Fresenius Medical Care Capital Trust IV                  7.875         06/15/11                 255,562
         515   HCA, Inc.                                                6.375         01/15/15                 513,786
          85   National Nephrology Associates, Inc., 144A - Private                                       
               Placement (a)                                            9.000         11/01/11                  94,669
         290   Team Health, Inc.                                        9.000         04/01/12                 284,925
         435   Tenet Healthcare Corp.                                   9.875         07/01/14                 454,575
                                                                                                          -------------

                                                                                                             5,018,417
                                                                                                          -------------





                                                                                               
               HOUSING   9.9%                                      
       1,240   Associated Materials, Inc. (f)                        0/11.250         03/01/14                 868,000
         625   Interface, Inc.                                          9.500         02/01/14                 660,937
         615   Nortek, Inc.                                             8.500         09/01/14                 596,550
         690   Ply Gem Industries, Inc.                                 9.000         02/15/12                 655,500
         340   Propex Fabrics, Inc.                                    10.000         12/01/12                 338,300
         445   RMCC Acquisition Co., 144A - Private                                       
               Placement (a)                                            9.500         11/01/12                 438,325
         290   Technical Olympic USA, Inc.                              7.500         01/15/15                 269,700
         370   Technical Olympic USA, Inc.                              9.000         07/01/10                 384,800
         290   Technical Olympic USA, Inc.                              9.000         07/01/10                 303,050
         310   Technical Olympic USA, Inc.                             10.375         07/01/12                 341,000
                                                                                                          -------------
                                                                                                             4,856,162
                                                                                                          -------------
                                                                    
               INFORMATION TECHNOLOGY   4.9%                                   
         445   Iron Mountain, Inc.                                      7.750         01/15/15                 441,662
         770   Iron Mountain, Inc.                                      8.625         04/01/13                 781,550
         405   Sanmina-SCI Corp., 144A - Private Placement (a)          6.750         03/01/13                 381,712
         800   Xerox Corp.                                              7.125         06/15/10                 831,000
                                                                                                          -------------
                                                                                                             2,435,924
                                                                                                          -------------
                                                                    
               MANUFACTURING   4.6%                                
         155   Flowserve Corp.                                         12.250         08/15/10                 169,337
         530   JohnsonDiversey, Inc.                                    9.625         05/15/12                 572,400
         439   Manitowoc, Inc.                                         10.500         08/01/12                 500,460
       1,010   Trimas Corp.                                             9.875         06/15/12               1,035,250
                                                                                                          -------------
                                                                                                             2,277,447
                                                                    
               METAL/GLASS CONTAINERS   3.0%                                    
       1,350   Owens-Brockway Glass Containers, Inc.                    8.875         02/15/09               1,447,875
                                                                                                          -------------
                                                                    
               METALS   4.2%                                       
         202   Doe Run Resources Corp. (Acquired 02/15/01 to                                      
               10/15/04, Cost $177,470) (e) (g) (h)                    13.063         11/01/08                 189,094
         140   Foundation PA Coal Co.                                   7.250         08/01/14                 142,800
         210   General Cable Corp.                                      9.500         11/15/10                 232,050
         690   Novelis, Inc. - 144A - Private Placement (Canada) (a)    7.250         02/15/15                 679,650
         440   UCAR Finance, Inc.                                      10.250         02/15/12                 473,000
         337   United States Steel Corp.                                9.750         05/15/10                 374,913
                                                                                                          -------------
                                                                                                             2,091,507
                                                                                                          -------------
                                                                    
               RETAIL   2.1%                                       
         500   General Nutrition Center, Inc.                           8.500         12/01/10                 427,500
         590   Petro Stopping Center Financial                          9.000         02/15/12                 610,650
                                                                                                          -------------
                                                                                                             1,038,150
                                                                                                          -------------





                                                                                               
                                                                    
               SERVICES   6.5%                                     
          45   Allied Waste North America, Inc.                         7.875         04/15/13                  45,113
         550   Allied Waste North America, Inc.                         8.500         12/01/08                 566,500
         950   Allied Waste North America, Inc.                         8.875         04/01/08                 986,813
         510   Buhrmann US, Inc.                                        8.250         07/01/14                 527,850
         170   Buhrmann US, Inc., 144A - Private Placement (a)          7.875         03/01/15                 170,850
         405   MSW Energy Holdings II LLC                               7.375         09/01/10                 413,100
          85   MSW Energy Holdings LLC                                  8.500         09/01/10                  89,675
         390   United Rentals North America, Inc.                       6.500         02/15/12                 381,225
                                                                                                          -------------
                                                                                                             3,181,126
                                                                                                          -------------
                                                                    
               TELECOMMUNICATIONS   6.1%                                                 
         760   Axtel SA (Mexico)                                       11.000         12/15/13                 807,500
         280   Exodus Communications, Inc. (c) (d) (e)                 11.250         07/01/08                       0
         430   Qwest Communications International, Inc., 144A - 
               Private Placement (a) (b)                                6.294         02/15/09                 435,375
         710   Qwest Corp.                                              6.625         09/15/05                 717,100
         575   Qwest Corp., 144A - Private Placement (a)                7.875         09/01/11                 595,125
         455   Valor Telecommunications Enterprise, 144A - Private                                    
               Placement (a)                                            7.750         02/15/15                 455,000
                                                                                                          -------------
                                                                                                             3,010,100
                                                                                                          -------------
                                                                    
               TRANSPORTATION   5.9%                               
         450   AutoNation, Inc.                                         9.000         08/01/08                 497,250
         585   Laidlaw International, Inc.                             10.750         06/15/11                 665,438
       1,065   Sonic Automotive, Inc.                                   8.625         08/15/13               1,065,000
         605   TRW Automotive, Inc.                                     9.375         02/15/13                 653,400
                                                                                                          -------------
                                                                                                             2,881,088
                                                                                                          -------------
                                                                    
               UTILITY   12.7%                                     
         485   AES Corp.                                                7.750         03/01/14                 503,188
          23   AES Corp.                                                8.875         02/15/11                  25,013
          73   AES Corp.                                                9.375         09/15/10                  80,848
         350   CMS Energy Corp.                                         6.300         02/01/12                 340,506
          65   CMS Energy Corp.                                         7.500         01/15/09                  67,275
         405   CMS Energy Corp.                                         8.500         04/15/11                 439,425
         605   Dynegy Holdings, Inc.                                    6.875         04/01/11                 539,963
         345   Dynegy Holdings, Inc., 144A - Private Placement (a)      9.875         07/15/10                 371,306
         235   IPALCO Enterprises, Inc.                                 8.625         11/14/11                 270,838
         485   Monongahela Power Co.                                    5.000         10/01/06                 490,329
         290   Nevada Power Co.                                         8.250         06/01/11                 323,350
         490   Nevada Power Co.                                         9.000         08/15/13                 552,475
         345   PSEG Energy Holdings, Inc.                               7.750         04/16/07                 356,213
          20   PSEG Energy Holdings, Inc.                               8.625         02/15/08                  21,200
         875   Reliant Energy, Inc.                                     6.750         12/15/14                 820,313
         195   Southern Natural Gas Co.                                 8.875         03/15/10                 212,414
         785   TNP Enterprises, Inc.                                   10.250         04/01/10                 830,138
                                                                                                          -------------
                                                                                                             6,244,794
                                                                                                          -------------







                                                                                               
               WIRELESS COMMUNICATIONS   6.4%                               
       1,025   Nextel Communications, Inc.                              6.875         10/31/13               1,073,688
         205   Rogers Wireless Communications, Inc. (Canada)            8.000         12/15/12                 211,663
         295   Rogers Wireless Communications, Inc., 144A - Private                                       
               Placement (Canada) (a)                                   7.500         03/15/15                 306,063
         250   Rural Cellular Corp. (b)                                 7.510         03/15/10                 257,500
         575   Rural Cellular Corp.                                     8.250         03/15/12                 589,375
         670   SBA Communications Corp., 144A - Private                                
               Placement (a)                                            8.500         12/01/12                 696,800
                                                                                                          -------------
                                                                                                             3,135,089
                                                                                                          -------------
                                                                  
TOTAL CORPORATE BONDS    167.2%                                                                             82,415,035
                                                                                                          -------------
                                                      
                                                   
DESCRIPTION                                                                                                 VALUE
                                                   
EQUITIES   0.9%                                   
               DecisionOne Corp. (3,033 common shares) (e) (i)                                                       0
               DecisionOne Corp. (6,670 common stock warrants)
               (e) (i)                                                                                               0
               Doe Run Resources Corp. (1 common stock warrant) 
               (e) (i)                                                                                               0

               HCI Direct, Inc. (30,357 common shares) (e) (i)                                                 455,355
               Hosiery Corp of America, Inc. (500 common shares)
               (e) (i)                                                                                               0

               VS Holdings, Inc. (11,316 common shares) (e) (i)                                                      0
                                                                                                          -------------
                   
TOTAL EQUITIES                                                                                                 455,355
                                                                                                          -------------
                                             
TOTAL LONG-TERM INVESTMENTS   168.1%  
   (Cost $84,356,510)                                                                                       82,870,390
                                             
REPURCHASE AGREEMENT   4.3%                 
               State Street Bank & Trust Co. ($2,107,000 par
               collateralized by U.S. Government obligations in a
               pooled cash account, interest rate of 2.70%, dated
               03/31/05, to be sold on 04/01/05 at $2,107,158)                                               2,107,000
                                                                                                          -------------
                               (Cost $2,107,000)
                                             
TOTAL INVESTMENTS   172.4%                  
   (Cost $86,463,510)                                                                                       84,977,390
                                          
OTHER ASSETS IN EXCESS OF LIABILITIES   4.0%                                                                 1,926,331
                                             
PREFERRED SHARES (INCLUDING ACCRUED DISTRIBUTIONS)   (76.4%)                                               (37,606,705)
                                                                                                          -------------
                                             
NET ASSETS APPLICABLE TO COMMON SHARES   100.0%                                                            $49,297,016
                                                                                                          -------------


               Percentages are calculated as a percentage of net assets 
               applicable to common shares.
(a)            144A securities are those which are exempt from
               registration under Rule 144A of the Securities Act of
               1933, as amended.  These securities may only be 
               resold in transactions exempt from registration which
               are normally those transactions with qualified
               institutional buyers.
(b)            Variable rate security.  Interest rate shown is that in
               effect at March 31, 2005.
(c)            Non-income producing as security is in default.
(d)            This borrower has filed for protection in federal
               bankruptcy court.







(e)            Market value is determined in accordance with
               procedures established in good faith by the Board of
               Trustees.
(f)            Security is a "step-up" bond where the coupon
               increases or steps up at a predetermined date.
(g)            Payment-in-kind security.
(h)            These securities are restricted and may be resold 
               only in transactions exempt from registration which 
               are normally those transactions with qualified
               institutional buyers.  Restricted securities comprise
               0.4% of net assets applicable to common shares.
(i)            Non-income producing security.
                  
                                   
  


Item 2.  Controls and Procedures.

(a) The Trust's principal executive officer and principal financial officer have
concluded that the Trust's disclosure controls and procedures are sufficient to
ensure that information required to be disclosed by the Trust in this Form N-Q
was recorded, processed, summarized and reported within the time periods
specified in the Securities and Exchange Commission's rules and forms, based
upon such officers' evaluation of these controls and procedures as of a date
within 90 days of the filing date of the report.

(b) There were no changes in the Trust's internal control over financial
reporting that occurred during the registrant's fiscal quarter that has
materially affected, or is reasonably likely to materially affect, the Trust's
internal control over financial reporting.

Item 3.  Exhibits.

(a)      A certification for the Principal Executive Officer of the registrant 
is attached hereto as part of EX-99.cert.

(b)      A certification for the Principal Financial Officer of the registrant 
is attached hereto as part of EX-99.cert.






SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

(Registrant)  Van Kampen High Income Trust

By: /s/ Ronald E. Robison
    ---------------------
Name: Ronald E. Robison
Title: Principal Executive Officer
Date: May 19, 2005

Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed by the following
persons on behalf of the registrant and in the capacities and on the dates
indicated.

By: /s/ Ronald E. Robison
    ---------------------
Name: Ronald E. Robison
Title: Principal Executive Officer
Date: May 19, 2005 

By: /s/ James W. Garrett
    --------------------
Name: James W. Garrett
Title: Principal Financial Officer
Date: May 19, 2005