Exhibit A

June 19, 2012

Ms. Lynn Schweinfurth

7151 Kendallwood Drive

Dallas, TX 75240

Employment offer – Chief Financial Officer

Dear Lynn,

We are pleased that you have decided to join Fiesta Restaurant Group. Below are the terms of the offer of employment. Your signature at the end of this letter will acknowledge your agreement to those terms.

The position is Vice President, Chief Financial Officer of Fiesta Restaurant Group, Inc. (“Fiesta”), reporting to the Chief Executive Officer.

Your employment will commence on Monday, July 16, 2012.

Your annual base salary will be $320,000. This is paid on a monthly basis in advance at the rate of $26,667. Direct deposit is available if you so choose. You will be eligible for annual merit increases beginning in 2014, based upon recommendations of the CEO and the Compensation Committee of the Board of Directors of Fiesta.

You will participate in the Fiesta Executive Bonus Plan. Your maximum potential bonus is equal to 90% of your annual base salary. Your bonus for 2012, if earned, will be pro-rated. It is anticipated the Bonus plan will provide that a portion of the bonus will be determined by achievement of individual objectives and a portion determined based upon increases in “shareholder value” as that term is defined in the Executive Bonus Plan. Recognize that as a consequence of the spin-off of

Fiesta being completed earlier this year, there may be changes to the existing Executive Bonus Plan made by the Compensation Committee of the Board of Fiesta.

As a condition of employment with Fiesta, all employees are subject to our Mandatory Arbitration Program (“MAP”) to resolve any employment disputes. You will be provided with the materials explaining the terms and conditions of MAP, and will be required to execute an acknowledgement of your agreement to be subject to MAP.

Effective August 1, 2012, you will be eligible to participate in the Fiesta Corporation Deferred Compensation Plan subject to the plan requirements. A copy of the Plan is enclosed.

You and your dependants (as defined by plan documents) will be eligible to participate in the Fiesta’s Medical, Dental, Vision, Flexible Savings Account and Life Insurance plans. All benefits are per the plan documents. Your participation (if you elect) in these benefits will be effective August 1, 2012, provided you return the necessary completed forms. You will also be eligible for the Short Term and Long Term Disability Plans. This benefit, if elected, will be effective November 1, 2012. Your share of the cost for the benefits you elect will be deducted from your monthly paycheck.

Commencing with your employment with Fiesta Restaurant Group, you will be eligible for three weeks of vacation each year. At the end of your tenth year of employment, you will then be eligible for four weeks of vacation. In the event of your termination, payment for unused vacation time will be based on the Company’s vacation policy in effect at that time.

You will be reimbursed for all business expenses incurred in accordance with Company policy including mileage reimbursement for use of your personal auto on company business.

As you are aware, Fiesta is in the process of identifying the location of its corporate office. In the event the location of the Fiesta Corporate Office is other than in Dallas, Texas, a full relocation package will be provided.

In the event of a separation of employment not due to “Cause” (as defined in the attached Exhibit A to this letter), you will be provided a severance payment equal twelve (12) months’ of base salary, and you will be entitled to receive the prorated portion of your bonus (provided a bonus would otherwise have been payable) that would be based upon year end results for the Company (all net of applicable withholding amounts). Payment of such severance and bonus would be conditioned upon and in consideration of, your entering into a mutually acceptable settlement and release with the Company. There will be no severance in the event of a termination for Cause.

I am confident that you will find Fiesta a fulfilling and gratifying place to work. If the above is acceptable to you, please confirm your acknowledgement by signing below and returning a copy of this letter to me, via e-mail at ***@***.

Sincerely,

Fiesta Restaurant Group, Inc.

“Cause” means (i) the commission by employee of any act or omission that would constitute a felony or any crime of moral turpitude under Federal law or the law of the state or foreign law in which such action occurred, (ii) dishonesty, disloyalty, fraud, embezzlement, theft, disclosure of trade secrets or confidential information or other acts or omissions that result in a breach of fiduciary or other material duty to the Company and/or a Subsidiary, (iii) continued reporting to work or working under the influence of alcohol, an illegal drug, an intoxicant or a controlled substance which renders employee incapable of performing his or her material duties to the satisfaction of the Company and/or its Subsidiaries, or (iv) the employee’s substantial disregard in the performance of the employee’s duties and/or responsibilities with respect to the Company and/or a Subsidiary, which disregard shall continue after notice to the employee and a reasonable opportunity to cure such behavior.