PetroQuest Energy, Inc. INCENTIVE STOCK OPTION AGREEMENT

Exhibit 10.4

PetroQuest Energy, Inc.

INCENTIVE STOCK OPTION AGREEMENT

1. Grant of Stock Option. As of the Grant Date (identified in the award notice provided to the Optionee electronically with this Agreement (the “Award Notice”)), PetroQuest Energy, Inc., a Delaware corporation (the “Company”), hereby grants an Incentive Stock Option (the “Option”) to the Optionee (identified in the Award Notice), an employee of the Company, to purchase the number of shares of the Company’s common stock, $.001 par value per share (the “Common Stock”), identified in the Award Notice (the “Shares”), subject to the terms and conditions of this agreement (the “Agreement”) and the Company’s 2013 Incentive Plan effective March 29, 2013 (the “Plan”) which is hereby incorporated herein in its entirety by reference. The Shares, when issued to Optionee upon the exercise of the Option, shall be fully paid and nonassessable. The Option is an “incentive stock option” as defined in Section 422 of the Internal Revenue Code. The Optionee’s electronic acceptance of the Award Notice shall be Optionee’s agreement to be bound by the terms of the Award Notice, this Agreement and Plan with respect to the Option.

2. Definitions. All capitalized terms used herein shall have the meanings set forth in the Plan unless otherwise specifically provided herein. The Optionee’s Award Notice sets forth meanings for various capitalized terms used in this Agreement.

3. Option Term. The Option shall commence on the Grant Date (identified in the Award Notice) and terminate on the date immediately prior to the tenth (10th) anniversary of the Grant Date. The period during which the Option is in effect and may be exercised is referred to herein as the “Option Period.”

4. Option Price. The Option Price per Share is identified in the Award Notice.

5. Vesting. The total number of Shares subject to this Option shall vest in accordance with the Vesting Schedule as follows: 33.3% on the first anniversary of the Grant Date, 33.3% on the second anniversary of the Grant Date and 33.4% on the third anniversary of the Grant Date. The Shares may be purchased at any time after they become vested, in whole or in part, during the Option Period; provided, however, the Option may only be exercisable to acquire whole Shares. The right of exercise provided herein shall be cumulative so that if the Option is not exercised to the maximum extent permissible after vesting, the vested portion of the Option shall be exercisable, in whole or in part, at any time during the Option Period.

6. Method of Exercise. The Option is exercisable by delivery of a written notice to the attention of the Secretary of the Company at the address for notices to the Company provided below, signed by the Optionee, specifying the number of Shares to be acquired on, and the effective date of, such exercise. The Optionee may withdraw notice of exercise of this Option, in writing, at any time prior to the close of business on the business day preceding the proposed exercise date.

7. Method of Payment. The Option Price upon exercise of the Option shall be payable to the Company in full either: (i) in cash or its equivalent, or (ii) subject to prior approval by the Committee in its discretion, by tendering previously acquired Shares having an aggregate Fair Market Value (as defined in the Plan) at the time of exercise equal to the total Option Price (provided that the Shares must have been held by the Optionee for at least six (6) months prior to their tender to satisfy the Option Price), or (iii) subject to prior approval by the Committee in its discretion, by withholding Shares which otherwise would be acquired on exercise having an aggregate Fair Market Value at the time of exercise equal to the total Option Price (as determined pursuant to Section 2.3 of the Plan), or (iv) subject to prior approval by the Committee in its discretion, by a combination of (i), (ii), and (iii) above. Any payment in shares of Common Stock shall be effected by the delivery of such shares to the Secretary of the Company, duly endorsed in blank or accompanied by stock powers duly executed in blank, together with any other documents as the Secretary may require. If the payment of the Option Price is remitted partly in Shares, the balance of the payment of the Option Price shall be paid in either cash, certified check, bank cashiers’ check, or by wire transfer.

The Committee, in its discretion, may allow (i) a “cashless exercise” as permitted under Federal Reserve Board’s Regulation T, 12 CFR Part 220 (or its successor), and subject to applicable securities law restrictions and tax withholdings, or (ii) any other means of exercise which the Committee, in its discretion, determines to be consistent with the Plan’s purpose and applicable law.

As soon as practicable after receipt of a written notification of exercise and full payment, the Company shall deliver to or on behalf of the Optionee, in the name of the Optionee or other appropriate recipient, Share certificates for the number of Shares purchased under the Option. Such delivery shall be effected for all purposes when a stock transfer agent of the Company shall have deposited such certificates in the United States mail, addressed to Optionee or other appropriate recipient.

8. Restrictions on Exercise. The Option may not be exercised if the issuance of such Shares or the method of payment of the consideration for such Shares would constitute a violation of any applicable federal or state securities or other laws or regulations, including any such laws or regulations or Company policies respecting blackout periods, or any rules or regulations of any stock exchange on which the Common Stock may be listed.

9. Termination of Employment. Voluntary or involuntary termination of Employment and the death or Disability of Optionee shall affect Optionee’s rights under the Option as follows:

(a) Termination for Cause. The vested and non-vested portions of the Option shall expire on 12:01 am. (CST) on the date of termination of Employment and shall not be exercisable to any extent if Optionee’s Employment with the Company is terminated for Cause (as defined in the Plan at the time of such termination of Employment).

(b) Other Involuntary Termination or Voluntary Termination. If Optionee’s Employment with the Company is terminated for any reason other than for Cause, retirement, death or Disability (as defined in the Plan at the time of termination of Employment), then (i) the non-vested portion of the Option shall immediately expire on the termination date (ii) the vested portion of the Option shall expire to the extent not exercised within three (3) months after the date of such termination of Employment. In no event may the Option be exercised by anyone after the earlier of (i) the expiration of the Option Period or (ii) three (3) months after termination of Employment.

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(c) Death or Disability. If Optionee’s Employment with the Company is terminated by death or Disability, then the vesting of the Option will be accelerated and the entire Option shall be 100% vested on the date of termination of Employment and shall expire 365 calendar days after the date of such termination of Employment to the extent not exercised by Optionee or, in the case of death, by the person or persons to whom Optionee’s rights under the Option have passed by will or by the laws of descent and distribution or, in the case of Disability, by Optionee’s legal representative. In no event may the Option be exercised by anyone after the earlier of (i) the expiration of the Option Period or (ii) 365 days after Optionee’s death or termination of Employment due to Disability.

(d) Retirement. In the event of termination due to retirement, the vested portion of the Option shall expire on the earlier of (A) the Option Period or (B) three (3) months after the date of retirement, and the unvested portion of the Option shall expire.

(e) Change of Control. In the event of a “Change in Control” of the Company (as defined in the Plan) the vesting of the Option will be accelerated and the entire Option shall be 100% vested as of the date immediately preceding a Change in Control and the Option may be accelerated and the Option shall otherwise be affected as provided in the Plan at such time. In addition, notwithstanding anything herein to the contrary, in the event of a Change in Control and to the extent any portion of this is deemed to be a Nonstatutory Stock Option on account of the limitation in Section 2.2(f) of the Plan or in the future for any other reason it is deemed to be a Nonstatutory Stock Option, such portion of the Option shall remain exercisable for the until the earlier of the expiration of the Option Period or one year after the Optionee’s voluntary or involuntary termination from employment without Cause or Retirement.

10. Qualification as an Incentive Stock Option. The Optionee understands that the Option is intended to qualify as an “incentive stock option” within the meaning of Section 422 of the Code. The Optionee must meet certain holding periods under Section 422(a) of the Code to obtain the federal income tax treatment applicable to the exercise of incentive stock options and the disposition of Shares acquired thereby. The Optionee further understands that the exercise price of Shares subject to this Option has been set by the Committee at a price that the Committee determined to be not less than 100% (or, if the Optionee, at the Grant Date, owned more than 10% of the total combined voting power of the Company’s outstanding voting securities, 110%) of the Fair Market Value, as determined in accordance with the Plan, of a share of Common Stock on the Grant Date. The Optionee further understands and agrees, however, that neither the Company nor the Committee shall be liable or responsible for any additional tax liability incurred by the Optionee in the event that the Internal Revenue Service for any reason determines that this Option does not qualify as an “incentive stock option” within the meaning of the Code.

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11. Independent Legal and Tax Advice. Optionee acknowledges that the Company has advised Optionee to obtain independent legal and tax advice regarding the grant and exercise of the Option and the disposition of any Shares acquired thereby.

12. No Rights in Shares. Optionee shall have no rights as a stockholder in respect of the Shares until the Optionee becomes the record holder of such Shares.

13. Investment Representation. Optionee will enter into such written representations, warranties and agreements as Company may reasonably request in order to comply with any federal or state securities law. Moreover, any stock certificate for any Shares issued to Optionee hereunder may contain a legend restricting their transferability as determined by the Company in its discretion. Optionee agrees that Company shall not be obligated to take any affirmative action in order to cause the issuance or transfer of Shares hereunder to comply with any law, rule or regulation that applies to the Shares subject to the Option.

14. No Guarantee of Employment. The Option shall not confer upon Optionee any right to continued Employment with the Company or any subsidiary or affiliate thereof.

15. Withholding of Taxes. This Option is subject to and the Company shall have the right to take any action as may be necessary or appropriate to satisfy any federal, state, or local tax withholding obligations, including at the Committee’s discretion, to make deductions from the number of Shares otherwise deliverable upon exercise of the Option in an amount sufficient to satisfy withholding of any federal, state or local taxes required by law.

16. General.

(a) Notices. All notices under this Agreement shall be mailed or delivered by hand to the parties at their respective addresses set forth beneath their signatures below or at such other address as may be designated in writing by either of the parties to one another. Notices shall be effective upon receipt.

(b) Shares Reserved. Company shall at all times during the Option Period reserve and keep available under the Plan such number of Shares as shall be sufficient to satisfy the requirements of this Option.

(c) Nontransferability of Option. The Option granted pursuant to this Agreement is not transferable other than by will, the laws of descent and distribution. The Option will be exercisable during Optionee’s lifetime only by Optionee or by Optionee’s legal representative in the event of Optionee’s Disability. No right or benefit hereunder shall in any manner be liable for or subject to any debts, contracts, liabilities, obligations or torts of Optionee.

(d) Amendment and Termination. No amendment, modification or termination of the Option or this Agreement shall be made at any time without the written consent of Optionee and Company.

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(e) No Guarantee of Tax Consequences. The Company and the Committee make no commitment or guarantee that any federal or state tax treatment will apply or be available to any person eligible for benefits under the Option. The Optionee has been advised and been provided the opportunity to obtain independent legal and tax advice regarding the grant and exercise of the Option and the disposition of any Shares acquired thereby.

(f) Severability. In the event that any provision of this Agreement shall be held illegal, invalid, or unenforceable for any reason, such provision shall be fully severable, but shall not affect the remaining provisions of the Agreement, and the Agreement shall be construed and enforced as if the illegal, invalid, or unenforceable provision had not been included herein.

(g) Supersedes Prior Agreements. This Agreement shall supersede and replace all prior agreements and understandings, oral or written, between the Company and the Optionee regarding the grant of the Options covered hereby.

(h) Governing Law. The Option shall be construed in accordance with the laws of the State of Delaware without regard to its conflict of law provisions, to the extent federal law does not supersede and preempt Delaware law.

17. Counterparts and Electronic Execution by Optionee. This Agreement may be executed in multiple original counterparts, each of which shall be deemed an original, but all of which together shall constitute but one and the same instrument. Optionee’s electronic acceptance of the Award Notice shall be deemed to be Optionee’s execution and acceptance of this Agreement.

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IN WITNESS WHEREOF, the Company has caused this Agreement to be executed on its behalf by its duly authorized officer as of the Grant Date.