EXHIBIT 32.1

WRITTEN STATEMENT OF CHIEF EXECUTIVE OFFICER AND

CHIEF FINANCIAL OFFICER PURSUANT TO SECTION 906 OF THE

SARBANES — OXLEY ACT OF 2002

The undersigned, the Chief Executive Officer and the Chief Financial Officer of Hines Global REIT, Inc. (the “Company”), each hereby certifies that to his/her knowledge, on the date hereof:

(a) the Form 10-Q of the Company for the quarterly period ended June 30, 2012 filed on the date hereof with the Securities and Exchange Commission (the “Report”) fully complies with the requirements of Section l3(a) or 15(d) of the Securities Exchange Act of 1934; and

(b) information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date:   August 14, 2012                                  /s/ Charles N. Hazen

 Charles N. Hazen

 President and Chief Executive Officer

Date:   August 14, 2012                                  /s/ Ryan T. Sims

Ryan T. Sims

Chief Financial Officer and Secretary