Heartware International (HTWR) 10-K 2013 FY Annual report

Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We have issued our report dated March 2, 2014, with respect to the consolidated financial statements and internal control over financial reporting included in the Annual Report of HeartWare International, Inc. on Form 10-K for the year ended December 31, 2013. We hereby consent to the incorporation by reference of said report in the Registration Statements of HeartWare International, Inc. on Forms S-8 (File No. 333-155359, effective November 13, 2008, File No. 333-172424, effective February 24, 2011, File No. 333-184358, effective October 10, 2012, and File No. 333-193649, effective January 30, 2014), Forms S-3 (File No. 333-161417, effective December 3, 2009, and File No. 333-193646, effective January 30, 2014), and Form S-4 (File No. 333-180988, effective July 3, 2012).

/s/ Grant Thornton LLP

Fort Lauderdale, Florida

March 2, 2014