Exhibit 32.1

CERTIFICATION OF

CHIEF EXECUTIVE OFFICER

OF GROUP 1 AUTOMOTIVE, INC.

PURSUANT TO 18 U.S.C. § 1350

AS ADOPTED PURSUANT TO SECTION 906 OF THE

SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q for the period ended June 30, 2012 filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Earl J. Hesterberg, Chief Executive Officer of Group 1 Automotive, Inc. (the “Company”), hereby certify that:

1. The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Earl J. Hesterberg

Earl J. Hesterberg

Chief Executive Officer

Date: July 27, 2012