Exhibit 10.1

SECOND AMENDMENT TO THE

SECOND AMENDED AND RESTATED

HORNBECK OFFSHORE SERVICES, INC.

INCENTIVE COMPENSATION PLAN

This SECOND AMENDMENT TO THE SECOND AMENDED AND RESTATED HORBECK OFFSHORE SERVICES, INC. INCENTIVE COMPENSATION PLAN (this “Amendment”) is made effective as of the 24th day of June, 2010, by the Board of Directors (the “Board”) of Hornbeck Offshore Services, Inc. (the “Company”).

WHEREAS , the Company sponsors the Second Amended and Restated Hornbeck Offshore Services, Inc. Incentive Compensation Plan (the “Plan”);

WHEREAS , pursuant to Section 13.1 of the Plan, the Board may at any time amend the provisions of the Plan; and

WHEREAS , the Company desires to amend the Plan to (i) increase the number of shares of common stock that may be delivered pursuant to awards granted under the Plan, (ii) remove the discretion to reprice stock options and stock appreciation rights, and (iii) clarify certain provisions of the Plan as they relate to protecting the deductibility of compensation under Section 162(m) of the Internal Revenue Code of 1986, as amended.

NOW, THEREFORE, the Board hereby amends the Plan as follows:

1. Section 2.15 shall be amended to read in its entirety as follows:

“2.15 ‘ Effective Date ’ shall mean March 28, 2006.”

2. Section 2.28 shall be amended to read in its entirety as follows:

“2.28 ‘ Performance Measure ’ shall mean each of the business criteria the Company may use in establishing a Performance Goal. For purposes of the Plan, Performance Measures are limited to net income; cash flow; cash flow on investment; pre-tax or post-tax profit levels or earnings; operating income or earnings; return on investment; earned value added; expense reduction levels; free cash flow; free cash flow per share; earnings per share; net earnings per share; net earnings from continuing operations; sales growth; sales volume; economic profit; expense reduction; controlled expenses; return on assets; return on net assets; return on equity; return on capital; construction work in progress-adjusted return on invested capital (adjusted ROIC); return on sales; return on invested capital; organic revenue; growth in managed assets; total shareholder return; stock price; stock price appreciation; EBIT; adjusted EBIT; EBITDA; adjusted EBITDA; return in excess of cost of capital; profit in excess of cost of capital; operating profits; net operating profit after tax; operating margin; profit margin; adjusted revenue; revenue; net revenue; operating revenue; net cash provided by operating activities; net cash provided by operating activities per share; cash conversion percentage; new sales; net new sales; cancellations; gross margin; gross margin percentage; and revenue before deferral.”

3. Section 2.34 shall be amended to read in its entirety as follows:

“2.34 ‘ Plan ’ shall mean this Second Amended and Restated Hornbeck Offshore Services, Inc. Incentive Compensation Plan, as amended from time to time. The Plan is an amendment and restatement of the Hornbeck Offshore Services, Inc. Amended and Restated Incentive Compensation Plan, as amended from time to time, which was effective in 2003 and which was itself an amendment and restatement of the Hornbeck Offshore Services, Inc. Incentive Compensation Plan, as amended from time to time, which was effective in 1997.”

4. Section 4.1 shall be amended to increase the number of shares authorized under the Plan by 700,000 by replacing the first sentence with the following:

“The maximum number of shares of Common Stock that may be delivered pursuant to Awards granted under the Plan is 4,200,000 shares.”

5. Section 4.2 shall be amended to read in its entirety as follows:

“4.2 Maximum Individual Grants. Subject to Section 12 of the Plan, no Participant may receive during any calendar year Awards covering an aggregate of more than 411,000 shares of Common Stock. Subject to Section 12 of the Plan, no Participant may receive during any calendar year a cash award under Section 9 of the Plan that exceeds Two Million Dollars ($2,000,000.00).”

6. Section 5.2 shall be amended to read in its entirety as follows:

“5.2 Grant of Awards . The grant of an Award shall be authorized by the Committee or the Board and shall be evidenced by an Award agreement setting forth the type of Award or Awards being granted, the total number of Shares subject to the Award(s), the Stock Option price (if applicable), the restriction period (if applicable), the term of the Award, the date of the grant of the Award, and such other terms, provisions, limitations, and, if applicable, Performance Goals, as are approved by the Committee, but not inconsistent with the Plan. The Company shall execute an Award agreement with a Participant after the Committee approves the issuance of an Award. This Plan was originally submitted to and approved by the Company’s stockholders in 2006.”

If the Committee establishes a purchase price, if any, for an Award of Restricted Stock, the Participant must accept such Award within a period of thirty (30) days (or such shorter period as the Committee may specify) after the date of the grant of the Award by executing the applicable Award agreement and paying such purchase price.”

7. Section 9 shall be amended to read in its entirety as follows:

“9.1 General. The Committee may, in its sole and absolute discretion, grant to any eligible Consultant, non-employee Director or Employee of the Company or a Subsidiary, other forms of Awards based upon, payable in or otherwise related to, in whole or in part, the Common Stock, if the Committee, in its sole and absolute discretion, determines that such other form of Award is appropriate and not inconsistent with the purposes of this Plan. The types of Awards that may be issued under this Section 9 shall include but not be limited to restricted stock units, dividend equivalent rights, and Performance Awards.

2

The terms and conditions of such other forms of Award shall be specified in an Award agreement that sets forth the terms and conditions of such Award, including, but not limited to, the price, the vesting schedule, and any other conditions and restrictions as the Committee shall impose as are not inconsistent with the terms of the Plan. In no event shall the price per Share of any Award based upon, payable in or otherwise related to, in whole or in part, the Common Stock be less than the par value of such Share. To the extent that any Award issued under this Section 9 constitutes a “nonqualified deferred compensation plan” under Section 409A of the Code, then such Award shall be subject to the restrictions set forth in Subsection 9.2 hereof.

A Performance Award may consist of either or both, as the Committee or the Board may determine, of (i) the right to receive Shares or Restricted Stock, or any combination thereof, upon the attainment of specified Performance Goals, as the Committee or the Board may determine (“Performance Shares”), or (ii) the right to receive a fixed dollar amount payable in Shares, Restricted Stock, cash, or any combination thereof, upon the attainment of specified Performance Goals, as the Committee or the Board may determine (“Performance Units”). The Committee or the Board may grant Performance Awards, for such minimum consideration, if any, as may be required by applicable law or such greater consideration as may be determined by the Committee or the Board, in its sole discretion. Each Performance Award shall have its own terms and conditions, which shall be determined in the sole discretion of the Committee or the Board. The terms and conditions of Performance Awards shall be specified at the time of the grant and may include provisions establishing the Performance Period, the Performance Goals to be achieved during a Performance Period, the Performance Measures used to determine vesting or the lapsing of applicable forfeiture restrictions (including the acceleration thereof), whether Performance Awards are forfeited or vest upon termination of employment during a Performance Period and the maximum or minimum settlement values. If the Committee or the Board determines, in its sole discretion, that the established Performance Measures or objectives are no longer suitable because of a change in the Company’s business, operations, corporate structure or for other reasons that the Committee or Board deems satisfactory, the Committee or the Board may modify the Performance Measures or objectives and/or the Performance Period, subject to the provisions of Subsection 15.9 hereof. Awards of Performance Shares and/or Performance Units are subject to acceleration of vesting, termination of restrictions and termination in the same manner as Stock Options pursuant to Subsections 6.5 and 6.6 of this Plan. Performance Awards may be valued by reference to the Fair Market Value of a Share or according to any other formula or method deemed appropriate by the Committee or the Board, in its sole discretion, including, but not limited to, achievement of specific financial, production, sales, cost or earnings performance objectives that the Committee or the Board believes to be relevant or the Company’s performance or the performance of the Common Stock measured against the performance of the market, the Company’s industry segment or its direct competitors. Performance Awards may also be conditioned upon the applicable Participant remaining in the employ of the Company or one of its Subsidiaries for a specified period. Performance Awards may be payable in a single payment or in installments and may be payable at a specified date or dates or upon attaining the performance objective or objectives, as specified in the applicable Award agreement. The extent to which any applicable Performance Goal has been achieved shall be conclusively determined by the Committee or the Board in its sole discretion.”

3

5. Section 14 shall be amended to read in its entirety as follows:

“SECTION 14. AMENDMENTS AND ADJUSTMENTS TO AWARDS

The Committee or the Board may amend, modify or terminate any outstanding Award with the Participant’s consent at any time prior to payment or exercise in any manner not inconsistent with the terms of this Plan, including, without limitation, (i) to change the date or dates as of which and/or the terms and conditions pursuant to which (A) a Stock Option becomes exercisable or (B) a Performance Award is deemed earned or (ii) subject to the restrictions on repricing set forth below, to cancel an Award and grant a new Award in substitution therefor under such different terms and conditions as the Committee or the Board determines in its sole discretion to be appropriate including, but not limited to, having an exercise price per share which may be higher or lower than the exercise price per share of the cancelled Award. The Committee or the Board may also make adjustments in the terms and conditions of, and the criteria included in agreements evidencing Awards in recognition of, unusual or nonrecurring events (including, without limitation, the events described in Section 12 hereof) affecting the Company, or the financial statements of the Company or any Affiliate, or of changes in applicable laws, regulations or accounting principles, whenever the Committee or the Board determines that such adjustments are appropriate to prevent reduction or enlargement of the benefits or potential benefits intended to be made available pursuant to this Plan. Any provision of this Plan (other than Section 9.2) or any agreement regarding an Award to the contrary notwithstanding, but subject to the restrictions on repricing set forth below, the Committee or the Board may cause any Award granted to be cancelled in consideration of a cash payment or alternative Award made to the holder of such cancelled Award equal in value to the Fair Market Value of such cancelled Award; provided, no cash payment or alternative Award shall be made which would constitute an impermissible acceleration of a payment of deferred compensation under Code Section 409A. The determinations of value pursuant to this Section 14 shall be made by the Committee or the Board in its sole discretion.

Notwithstanding any provision in this Plan to the contrary, repricing of Stock Options and Stock Appreciation Rights shall not be permitted. For this purpose, a repricing means any of the following (or any other action that has the same effect as any of the following): (i) changing the terms of a Stock Option or a Stock Appreciation Right to lower its exercise price; (ii) any other action that is treated as a repricing under generally accepted accounting principles; and (iii) canceling a Stock Option or Stock Appreciation Right at a time when its exercise price is equal to or greater than the fair market value of the underlying Shares in exchange for another Stock Option, Stock Appreciation Right, Restricted Shares or other equity award. Such cancellation and exchange would be considered a repricing regardless of whether it is treated as a repricing under generally accepted accounting principles and regardless of whether it is voluntary on the part of the Participant.”

6. Except as set forth herein and as previously amended, the Plan shall continue in full force and effect.

* * * * *

4