Exhibit 23.2

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement (Form S-8) pertaining to the Acceleron Pharma Inc. 2003 Stock Option and Restricted Stock Plan and the Acceleron Pharma Inc. 2013 Equity Incentive Plan of our report dated July 3, 2013, except for Note 16, as to which the date is September 5, 2013, with respect to the financial statements of Acceleron Pharma Inc. included in the Registration Statement on Form S-1 as amended (File No. 333-190417) and related Prospectus filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Boston, Massachusetts

December 11, 2013