Filed Pursuant to Rule 497
Registration No. 333-178695

CLEARBRIDGE ENERGY MLP FUND INC.

SUPPLEMENT NO. 2 DATED December 23, 2014 TO

PROSPECTUS DATED APRIL 2, 2014

Recent developments

ClearBridge Energy MLP Fund Inc. (the “Fund”) announced that effective January 1, 2015, the Board of Directors of the Fund has appointed Robert D. Agdern as a member of the Board of Directors. In addition, Mr. Agdern has been appointed to the Fund’s Nominating Committee and Audit Committee.

Since 2002, Mr. Agdern has served a Member of the Advisory Committee of the Dispute Resolution Research Center at the Kellogg Graduate School of Business, Northwestern University. Mr. Agdern served as Deputy General Counsel of BP PLC from 1999 to 2001 and Associate General Counsel at Amoco Corporation from 1993 to 1998 (Amoco merged with British Petroleum in 1998 forming BP PLC).