Exhibit 13.1

CERTIFICATION OF THE CHIEF EXECUTIVE OFFICER

REQUIRED BY RULE 13A-14(B) AND SECTION 1350

OF CHAPTER 63 OF TITLE 18 OF THE UNITED STATES CODE,

AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and (b) of Section 1350 of Chapter 63 of Title 18 of the United States Code), the undersigned officer of Textainer Group Holdings Limited (the “Company”), hereby certifies, to such officer’s knowledge, that:

1. The Annual Report on Form 20-F for the year ended December 31, 2012 (the “Report”) of the Company fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

Date: March 15, 2013

/s/ PHILIP K. BREWER

Philip K. Brewer

President and Chief Executive Officer

(Principal Executive Officer)