Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We hereby consent to the incorporation by reference in the Registration Statements on Form S-8 (Nos. 33-23053, 33-38030, 33-65192, 333-38865, 333-66029, 333-103245, 333-114066, 333-123675 and 333-123676) of ABIOMED, Inc. of our report dated June 14, 2005 relating to the financial statements, management’s assessment of the effectiveness of internal control over financial reporting, which appears in this Annual Report on Form 10-K.

/s/ PricewaterhouseCoopers LLP

Boston, Massachusetts

June 14, 2005