Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We hereby consent to the incorporation by reference in the Registration Statement on Form S-8 Nos. 333-125926, 333-141807, 333-152755 and 333-159886, on Form S-3 Nos. 33-23053, 33-38030, 33-65192, 333-38865, 333-66029, 333-103245, 333-114066, 333-123675, 333-123676, 333-132054, 333-152989 and 333-176620 of our report dated May 31, 2012 relating to the financial statements of the ABIOMED Retirement Savings Plan, which appears in the Annual Report on Form 11-K of ABIOMED, Inc.

/s/ Farrar Gates & Green, LLC

Danvers, Massachusetts

May 31, 2012