FILING PURSUANT TO RULE 424(b)(2)
                                           REGISTRATION STATEMENT NO. 333-115195

                           PROSPECTUS SUPPLEMENT NO. 2
                        (TO PROSPECTUS DATED MAY 5, 2004)

                                GERON CORPORATION

                                  COMMON STOCK,
                      WARRANTS TO PURCHASE COMMON STOCK AND
                 COMMON STOCK ISSUABLE UPON EXERCISE OF WARRANTS

     You should read this prospectus supplement and the accompanying prospectus
carefully before you invest. Both documents contain information you should
consider carefully before making your investment decision.

     We are offering pursuant to the terms and conditions of a common stock
purchase agreement an aggregate of 740,741 shares of our common stock, par value
$0.001 per share, warrants to purchase an aggregate of 370,370 additional shares
of common stock and the shares of our common stock to be issued upon exercise of
such warrants. We will receive immediate proceeds from the sale of these shares
and warrants equal to approximately $4,000,000, less our expenses relating to
the sale, which are estimated to be $25,000. The shares were sold at $5.40 per
share.

     The warrants are exercisable from time to time at a price of $7.95 per
share during the period from April 22, 2005 until April 22, 2010. We will
receive additional proceeds of approximately $2.9 million upon the full exercise
of warrants.

     There will be no warrant agent in connection with the issuance of the
warrants.

                                USE OF PROCEEDS

     We intend to use the net proceeds from the sale of securities under this
prospectus supplement primarily for general working capital purposes, including
to fund our financial commitment to TA Therapeutics. Ltd.

                LIMITATION ON THE USE OF OUR NET OPERATING LOSSES

We have significant amounts of net operating loss ("NOL") carry forwards
(including, as of December 31, 2004, domestic federal NOL carry forwards of
approximately $245,000,000, which will expire at various dates beginning 2006
through 2024, if not utilized). These NOLs may be used to offset future taxable
income, to the extent we generate any taxable income, and thereby reduce or
eliminate our future federal income taxes otherwise payable. However, the
Internal Revenue Code of 1986, as amended, imposes significant limitations on
the utilization of NOLs in the event of an "ownership change," as defined in
Section 382 of the Code. This Section 382 limitation is an annual limitation on
the amount of pre-ownership change NOLs that a corporation may use to offset its
post-ownership change income. We may or may not have experienced an ownership
change as a result of events in the past and/or the sale of shares of common
stock and warrants pursuant to this prospectus supplement (or a combination
thereof). If so, the use of our NOLs (or a portion thereof) against our future
taxable income may be subject to a limitation under Section 382.

                    MATERIAL U.S. FEDERAL TAX CONSIDERATIONS

     The following is a general discussion of the material U.S. federal income
tax consequences of the ownership and disposition of our common stock and
warrants, but is not a complete analysis of all the potential tax consequences
relating thereto. For the purposes of this discussion, a U.S. Holder is any
beneficial owner of our common stock or warrants that is treated for U.S.
federal income tax purposes as:




     o    an individual citizen or resident of the United States;

     o    a corporation (or other entity taxable as a corporation) created or
          organized in the United States or under the laws of the United States
          or any political subdivision thereof;

     o    an estate whose income is subject to U.S. federal income tax
          regardless of its source; or

     o    a trust (x) if a court within the United States is able to exercise
          primary supervision over the administration of the trust and one or
          more United States persons have the authority to control all
          substantial decisions of the trust or (y) which has made a valid
          election to be treated as a United States person.

     If a partnership holds our common stock or warrants, the tax treatment of a
partner will generally depend on the status of the partner and upon the
activities of the partnership. Accordingly, partnerships which hold our common
stock and partners in such partnerships should consult their own tax advisors.

     This discussion does not address all aspects of U.S. federal income
taxation that may be relevant in light of a U.S. holder's special tax status or
special circumstances. U.S. expatriates, insurance companies, tax-exempt
organizations, dealers in securities, insurance companies, banks or other
financial institutions, "controlled foreign corporations," "passive foreign
investment companies," corporations that accumulate earnings to avoid U.S.
federal income tax, U.S. expatriates, U.S. Holders whose functional currency is
not the U.S. dollar, tax-exempt organizations, and investors that hold our
common stock as part of a hedge, straddle or conversion transaction are among
those categories of potential investors that are subject to special rules not
covered in this discussion. This discussion does not address any tax
consequences arising under the laws of any state, local or non-U.S. taxing
jurisdiction. Furthermore, the following discussion is based on current
provisions of the Internal Revenue Code of 1986, as amended, and Treasury
Regulations and administrative and judicial interpretations thereof, all as in
effect on the date hereof, and all of which are subject to change, possibly with
retroactive effect. Accordingly, each Non-U.S. Holder should consult its own tax
advisors regarding the U.S. federal, state, local and non-U.S. income and other
tax consequences of acquiring, holding and disposing of shares of our common
stock.

U.S. HOLDERS

Dividends Paid on Common Stock

     A U.S. Holder generally will be required to include in gross income as
ordinary dividend income the amount of any distributions paid on the common
stock to the extent that such distributions are paid out of our current or
accumulated earnings and profits as determined for U.S. federal income tax
purposes. Distributions in excess of such earnings and profits will reduce the
U.S. Holder's tax basis in its common stock and, to the extent such excess
distributions exceed such tax basis, will be treated as gain from a sale or
exchange of such common stock. Corporate holders may be entitled to a dividends
received deduction with respect to such distributions and are urged to consult
their own tax advisors in this regard. With respect to non-corporate U.S.
Holders for taxable years beginning before January 1, 2009, dividends may be
taxed at the lower applicable capital gains rate provided that certain holding
period requirements are met.

Disposition of Common Stock

     Upon the sale or other disposition of common stock, a U.S. Holder generally
will recognize capital gain or loss equal to the difference between the amount
realized on the sale and such holder's adjusted tax basis in the common stock. A
U.S. Holder's tax basis in its common stock will equal that portion of the cost
of the Unit that is allocated to the common stock (based on the relative fair
market values of the common stock and the warrant comprising the Unit). Gain or
loss upon the disposition of the common stock will be a long-term if, at the
time of the disposition, the holding period for the common stock exceeds on
year.




Tax Treatment of Warrants

     A U.S. Holder will recognize gain or loss upon the sale, redemption, lapse
or other taxable disposition of a warrant in an amount equal to the difference
between the amount of cash and the fair market value of other property received
(if any) by the U.S. Holder and the U.S. Holder's tax basis in the warrant. A
U.S. Holder's tax basis in a warrant will equal that portion of the cost of the
Unit that is allocated to the warrant (based on the relative fair market values
of the common stock and the warrant comprising the Unit). Such gain or loss will
be capital gain or loss if the common stock to which the warrants relate would
be a capital asset in the hands of the warrant holder and will be long-term
capital gain or loss if the holding period exceeds one year.

     The cash exercise of a warrant will not be a taxable event for the
exercising U.S. Holder, except with respect to cash, if any, received in lieu of
a fractional share. A U.S. Holder will generally have a holding period in shares
of common stock acquired upon exercise of a warrant that commences on the day
after the date of exercise of the warrant.

     If the exercise price is nominal, it is possible that the warrants may be
deemed to have been exercised for tax purposes on the date on which they first
became exercisable or possibly on the date issued, regardless of whether they
are actually exercised on the date on which they are first exercisable. As a
result, it is possible that the holding period of shares of common stock may be
deemed to have begun on the date on which the warrants first became exercisable
or possibly on the date issued.

     An adjustment to the exercise price or conversion ratio of the warrants, or
the failure to make such adjustments, may in certain circumstances result in
constructive distributions to the holders of the warrants that could be taxable
as dividends under Section 305 of the Code. In such event, a holder's tax basis
in the warrant would be increased by the amount of any such dividend.

NON-U.S. HOLDERS

     A Non-U.S. Holder is a beneficial owner of our common stock or warrants
that is not a U.S. Holder or a U.S. domestic partnership or other entity treated
as a U.S. domestic partnership for U.S. federal income tax purposes.

Dividends Paid on Common Stock

     Payments on our common stock will constitute dividends for U.S. federal
income tax purposes to the extent paid from our current or accumulated earnings
and profits, as determined under U.S. federal income tax principles. Amounts not
treated as dividends for U.S. federal income tax purposes will constitute a
return of capital and will first be applied against and reduce a holder's
adjusted basis in the common stock, but not below zero, and then the excess, if
any, will be treated as gain from the sale of the common stock (the tax
treatment of which is described below).

     Amounts treated as dividends paid to a Non-U.S. Holder of common stock
generally will be subject to U.S. withholding tax either at a rate of 30% of the
gross amount of the dividends or such lower rate as may be specified by an
applicable tax treaty. In order to receive a reduced treaty rate, a Non-U.S.
Holder must provide a valid IRS Form W-8BEN or other successor form certifying
qualification for the reduced rate.




     Dividends received by a Non-U.S. Holder that are effectively connected with
a United States trade or business conducted by the Non-U.S. Holder are exempt
from such withholding tax. In order to obtain this exemption, a Non-U.S. Holder
must provide a valid IRS Form W-8ECI or other successor form properly certifying
such exemption. Such effectively connected dividends, although not subject to
withholding tax, are generally taxed at the same graduated rates applicable to
United States persons, net of allowable deductions and credits.

     In addition to the graduated tax described above, dividends received by a
corporate Non-U.S. Holder that are effectively connected with a United States
trade or business of such holder may also be subject to a branch profits tax at
a rate of 30% or such lower rate as may be specified by an applicable tax
treaty.

     A Non-U.S. Holder may obtain a refund of any excess amounts currently
withheld if an appropriate claim for refund is filed timely with the IRS. If a
Non-U.S. Holder holds our common stock through a foreign partnership or a
foreign intermediary, the foreign partnership or foreign intermediary will also
be required to comply with additional certification requirements.

Gain on Disposition of Common Stock or Warrants

     A Non-U.S. Holder generally will not be subject to U.S. federal income tax
on any gain realized upon the sale or other disposition of our common stock or
warrants unless:

     o    the gain is effectively connected with a United States trade or
          business of the Non-U.S. Holder or, if a tax treaty applies, as
          attributable to a United States permanent establishment maintained by
          such non-United States holder;

     o    the Non-U.S. Holder is an individual who holds his or her common stock
          or warrants as a capital asset (generally, an asset held for
          investment purposes) and who is present in the United States for a
          period or periods aggregating 183 days or more during the taxable year
          in which the sale or disposition occurs and other conditions are met;
          or

     o    our common stock or warrants constitute a United States real property
          interest by reason of our status as a "United States real property
          holding corporation" (a "USRPHC") for U.S. federal income tax purposes
          at any time within the shorter of the five-year period preceding the
          disposition or the holder's holding period for our common stock.

     We believe that we are not currently and do not expect to become a USRPHC.
However, because the determination of whether we are a USRPHC depends on the
fair market value of our United States real property interests relative to the
fair market value of our other business assets, there can be no assurance that
we will not become a USRPHC in the future.

     Unless an applicable treaty provides otherwise, gain described in the first
bullet point above will be subject to U.S. federal income tax imposed on net
income on the same basis that applies to United States persons generally and,
for corporate holders under certain circumstances, the branch profits tax, but
will generally not be subject to withholding. Non-U.S. Holders should consult
any applicable income tax treaties that may provide for different rules.




     Our common stock is quoted on the Nasdaq National Market under the symbol
"GERN." On April 21, 2005, the last reported sale price of our common stock on
the Nasdaq National Market was $6.62 per share. As of April 21, 2005, we had
54,694,840 shares of common stock outstanding.

     Investing in our common stock involves certain risks. See "Risk Factors"
beginning on page 1 of the prospectus, including the specific risks set forth
under the caption "Additional Factors That May Affect Future Results" and
incorporated by reference from the Company's filings made with the Securities
and Exchange Commission under the Securities Exchange of Act, as amended,
between the date of the prospectus and the termination of the offering.

     You should rely on the information provided or incorporated by reference in
this prospectus supplement and the prospectus. We have not authorized anyone
else to provide you with different information. You should not assume that the
information in this prospectus supplement is accurate as of any date other than
the date on the front of these documents.

     Neither the U.S. Securities and Exchange Commission nor any state
securities commission has approved or disapproved of the securities or passed
upon the accuracy or adequacy of this prospectus. Any representation to the
contrary is a criminal offense.

     The date of this prospectus supplement is April 22, 2005.

                                TABLE OF CONTENTS

                                   PROSPECTUS

About this Prospectus                                                         1
About Geron                                                                   1
Risk Factors                                                                  1
Forward-Looking Statements                                                    2
Ratio of Earnings to Fixed Charges                                            2
Use of Proceeds                                                               2
Plan of Distribution                                                          2
Description of Debt Securities                                                4
Description of Common Stock                                                  12
Description of Preferred Stock                                               13
Description of Warrants                                                      15
Certain Provisions of Delaware Law and of the Company's Charter and Bylaws   16
Legal Matters                                                                17
Experts                                                                      17
Limitation on Liability and Disclosure of Commission Position on
 Indemnification for Securities Act Liabilities                              17
Where You Can Find More Information                                          18