Exhibit 32.1

CERTIFICATION

PURSUANT TO

SECTION 1350 OF CHAPTER 63 OF TITLE 18 OF THE UNITED STATES CODE

I, Jeff Baisley, Chief Financial Officer of Graham Capital Management L.P. and I, Paul Sedlack, Chief Executive Officer of Graham Capital Management L.P., certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that:

1. The Annual Report on Form 10-K of Graham Alternative Investment Fund II LLC (the “registrant”) for the year ended December 31, 2012 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 registrant.

Date: March 28, 2013

/s/ Jeff Baisley

Jeff Baisley

Chief Financial Officer

Graham Capital Management L.P.

/s/ Paul Sedlack

Paul Sedlack

Chief Executive Officer

Graham Capital Management L.P.