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Exhibit 23.1

Consent of Independent Registered Public Accounting Firm
We consent to the incorporation by reference in the following Registration Statements:

(1)
Registration Statement (Form S-8 No. 333-192789) pertaining to the Acceleron Pharma Inc. 2003 Stock Option and Restricted Stock Plan and the Acceleron Pharma Inc. 2013 Equity Incentive Plan,

(2)
Registration Statement (Form S-8 No. 333-198259) pertaining to the Acceleron Pharma Inc. 2013 Employee Stock Purchase Plan and the Acceleron Pharma Inc. 2013 Equity Incentive Plan,

(3)
Registration Statement (Form S-8 No. 333-203354) pertaining to the Acceleron Pharma Inc. 2013 Equity Incentive Plan,

(4)
Registration Statement (Form S-8 No. 333-211867) pertaining to the Acceleron Pharma Inc. 2013 Equity Incentive Plan,

(5)
Registration Statement (Form S-8 No. 333-219661) pertaining to the Acceleron Pharma Inc. 2013 Equity Incentive Plan,

(6)
Registration Statement (Form S-3 No. 333-220522) of Acceleron Pharma Inc.,

(7)
Registration Statement (Form S-8 No. 333-223270) pertaining to the Acceleron Pharma Inc. 2013 Equity Incentive Plan, and

(8)
Registration Statement (Form S-8 No. 333-229911) pertaining to the Acceleron Pharma Inc. 2013 Equity Incentive Plan;

of our reports dated February 27, 2020, with respect to the consolidated financial statements of Acceleron Pharma Inc. and the effectiveness of internal control over financial reporting of Acceleron Pharma Inc. included in this Annual Report (Form 10-K) of Acceleron Pharma Inc. for the year ended December 31, 2019.
 
 
/s/ Ernst & Young LLP
Boston, Massachusetts
February 27, 2020