SUBORDINATE SECURED PROMISSORY NOTE

Exhibit 10.1

THIS NOTE HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”) OR ANY STATE SECURITIES LAWS. IT MAY NOT BE SOLD, OFFERED FOR SALE, TRANSFERRED, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR AN EXEMPTION THEREFROM. THE COMPANY MAY REQUIRE AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT ANY PROPOSED TRANSER OR RESALE IS IN COMPLIANCE WITH THE SECURITIES ACT.

SUBORDINATE SECURED PROMISSORY NOTE

      FOR VALUE RECEIVED , Infinity Energy Resources, Inc., a Delaware corporation (the “Company”), promises to pay to the order of Off-Shore Finance, LLC, a Nevada limited liability company (the “Holder”), the principal sum of One Million Two Hundred Seventy Five Thousand Dollars (US$1,275,000) or, if less, the aggregate unpaid principal amount loaned and outstanding when due, whether upon the Maturity Date, as defined below, acceleration, redemption or otherwise (the “Note”) (in each case in accordance with the terms thereof). Payment of the Note will be secured by (i) two second-lien Deeds of Trust and Security Agreements dated March 23, 2009 (collectively, the “Security Agreement”), by and between Infinity Oil and Gas of Texas, Inc. and Infinity Oil and Gas of Wyoming, Inc., respectively, and the Buyer, covering certain collateral as more particularly described therein and (ii) a Commercial Guaranty by each of Infinity Oil and Gas of Texas, Inc. and Infinity Oil & Gas of Wyoming, Inc. in favor of Holder (the “Commercial Guaranties”) and the Note is further subject to a Subordination and Intercreditor Agreement dated March 23, 2009 (the “Subordination Agreement”), by and among the Holder, the Company and Amegy. This Note is issued in connection with that certain Securities Purchase Agreement, dated March 23, 2009 between the Company and the Holder (the “Purchase Agreement”) and any terms used but not defined in this Note shall have the definitions assigned to them in the Purchase Agreement.

     The Company agrees to pay interest on the outstanding unpaid principal amount of the Note at a rate of 6.0% per annum (“Interest”) from the date of borrowing, and continuing until paid in accordance with the provisions of this Note, subject, however, to the provisions of the Subordination Agreement. Interest on this Note shall be computed on the basis of a 360-day year and actual days elapsed. Amounts are deemed borrowed under the Note as follows:

     1. For amounts loaned under Section 2 hereof, as of the date such funds are deposited in the Company’s operating account at U.S. Bank.

     2. For amounts required to be funded by Holder by Amegy under Section 1.3(c) of the Off-Shore Escrow Agreement, as of the date such funds are transferred out of the Off-Shore Escrow Account.

     The Loan Origination Fee and all Commitment Fees (as charged to the Company from time to time as provided in the Purchase Agreement) shall be deemed accrued interest hereunder.

     1.  Payment of Principal and Interest . The entire unpaid balance of principal and all unpaid and accrued interest shall become fully due and payable on March 23, 2012 (the “Maturity Date”) or such earlier date as the maturity hereof shall be accelerated in accordance with the terms of Section 3 below. The principal and unpaid accrued Interest under this Note may be prepaid, in whole or in part, in cash, at any time and from time to time, without penalty, in the sole discretion of the Company by fifteen (15) days prior notice.

     2.  Draw Down Procedure . The Holder shall make loans to the Company upon the Company’s request and in accordance with this Section 2, from time to time until the Maturity Date, provided that in no event shall the aggregate principal amount of such loans at any time exceed $1,275,000. A request for a loan, in substantially the form attached hereto as Exhibit 1 , shall be executed by the Company’s Chief Executive Officer or Chief Financial Officer and be delivered to the Holder, specifying the requested amount and date of the loan (a “Loan Request”). Prior to making any Loan Requests, the Company shall have submitted a budget to the Holder and Amegy for approval, setting forth the proposed use of the funds being borrowed hereunder (the “Approved Budget”). All items under the Approved Budget shall relate to the Company’s direct and indirect expenditures in connection with the concessions in the Tyra and Perlas Blocks, offshore Nicaragua, as awarded to the Company by the Republic of Nicaragua in 2003, as hereafter amended and modified (the “N