Exhibit 10.1

SECOND AMENDMENT TO THE

GASTAR EXPLORATION LTD.

2006 LONG-TERM STOCK INCENTIVE PLAN

WHEREAS, Gastar Exploration Ltd. (the “Company”) maintains the Gastar Exploration Ltd. 2006 Long-Term Stock Incentive Plan (the “Plan”);

WHEREAS, the Company desires to amend the Plan to (i) increase the number of shares available for awards under the Plan, and (ii) increase the individual annual award limit for Covered Employees for purposes of Section 162(m) of the Internal Revenue Code;

WHEREAS, pursuant to Section 16 of the Plan, the Company, by action of its Board of Directors, has the right to amend the Plan;

NOW, THEREFORE, effective as of June 3, 2012, the Plan is hereby amended as provided below; provided, however, that if this Second Amendment is not approved by the shareholders of the Company at the Company’s 2012 Annual Meeting of Shareholders, this Second Amendment shall not become effective:

1. Section 4 of the Plan is hereby deleted and the following substituted therefor:

“Subject to adjustment pursuant to Section 11(a) hereof, the total number of shares of Common Stock (“Shares”) that may be delivered pursuant to Awards granted under the Plan is increased by 5,000,000 Shares from 6,000,000 Shares (the 5,000,000 Shares originally authorized under the Plan and increased by the 25,000,000 Shares originally authorized under the Stock Option Plan of Gastar Exploration Ltd., which was merged into the Plan effective as of April 1, 2009, with such resulting 30,000,000 Shares then being adjusted to 6,000,000 to reflect the 1-for-5 reverse stock split effective August 3, 2009) to 11,000,000 Shares, with 100% of such Shares being available for incentive stock option grants under the Plan. If an Award is forfeited, lapses, expires, terminates or is canceled without the delivery of Shares or is settled in cash, then the Shares covered by such Award, to the extent of such forfeiture, expiration, lapse, termination, cancellation, or settlement in cash, shall again be Shares that may be delivered with respect to Awards granted under the Plan. The grant of “restricted” Shares of Bonus Stock that are subsequently forfeited, Shares that are withheld (“netted”) from an Award by the Company for the payment of the exercise price of the Award and Shares netted from an Award to satisfy the Company’s tax withholding obligations with respect to the Award shall not be considered to have been Shares “delivered” for this purpose and shall again be Shares that may be delivered with respect to Awards granted under the Plan.”

2. Section 6 of the Plan is hereby deleted and the following substituted therefor:

“The Shares available for Awards under the Plan may be delivered with respect to Options, Bonus Stock Awards and/or Stock Appreciation Rights granted under the Plan to any eligible individual(s); provided, however, that subject to Section 11(a), not more than 1.0 million Shares may be granted to any one Employee in any calendar year under all Awards granted to such Employee in that calendar year.”

Except as amended hereby, the Plan shall continue in full force and effect without change and the Plan and this Second Amendment shall be read, taken, and construed as one and the same instrument.