Exhibit 3.1

CERTIFICATE OF AMENDMENT

TO THE

CERTIFICATE OF DESIGNATION

OF THE

9.25% SERIES B CUMULATIVE PREFERRED STOCK

($0.001 PAR VALUE)

OF

GMX RESOURCES INC.

Pursuant to Section 1032 of the Oklahoma General Corporation Act, GMX RESOURCES INC., an Oklahoma corporation (“Corporation”), does hereby certify that the following resolutions were duly adopted by the Board of Directors of the Corporation on December 13, 2010:

WHEREAS, the Corporation filed a Certificate of Designation with the Oklahoma Secretary of State on August 8, 2006 (the “Certificate of Designation”), setting forth certain resolutions of the Corporation’s Board of Directors establishing the powers, preferences, rights and limitations of the Corporation’s 9.25% Series B Cumulative Preferred Stock, par value $0.001 per share (“Series B Preferred Stock”); and

WHEREAS, the Board of Directors deems it desirable and in the best interests of the Corporation to amend the terms of the Certificate of Designation to increase the number of authorized shares of Series B Preferred Stock from 3,000,000 shares to 6,000,000 shares;

RESOLVED, that the number of authorized shares of Series B Preferred Stock shall be and is hereby increased from 3,000,000 shares to 6,000,000 shares; and

FURTHER RESOLVED, that a Certificate of Amendment to the Certificate of Designation setting forth these resolutions shall be prepared, and the Executive Officers be, and each of them hereby is, authorized, empowered and directed on behalf of the Corporation and in its name to execute and to file the Certificate of Amendment to the Certificate of Designation with the Oklahoma Secretary of State.

IN WITNESS WHEREOF, the Corporation has caused this Certificate of Amendment to be duly executed on its behalf by the undersigned, Ken L. Kenworthy, Jr., Chief Executive Officer, and attested by James A. Merrill, its Secretary, this 13th day of December, 2010.