Filed Pursuant to Rule 497
Registration No. 333-178695

CLEARBRIDGE ENERGY MLP FUND INC.

SUPPLEMENT DATED MAY 2, 2014 TO

PROSPECTUS DATED APRIL 2, 2014

Recent developments

As previously disclosed in the Fund’s press release dated May 1, 2014, ClearBridge Energy MLP Fund Inc. (the “Fund”) completed a private placement of $75 million of fixed-rate senior secured notes on April 30, 2014. Net proceeds from the offering will be used to make new portfolio investments, and for general corporate purposes. Immediately after the note issuance, the Fund’s total leverage was $502 million or 20% of managed assets, composed of 88% in fixed-rate securities and 12% in floating rate financing.

The table below summarizes the key terms of the private placement.