Exhibit 10.1

Monolithic Power Systems, Inc.

6409 Guadalupe Mines Road

San Jose, CA 95120

Dr. Jeff Zhou

December 16, 2009

Dear Jeff,

I am pleased to offer you a seat on the Board of Directors (the “Board”) of Monolithic Power Systems, Inc. (the “Company”) as a Class II director and as a member of the Board’s Compensation Committee. Your appointment to the Board and the Compensation Committee will be effective on February 2, 2010. With the hope and expectation that you will accept this offer, I have summarized a few related matters below for your reference.

First, should you accept this offer, the Company will, upon the effective date of your joining the Board, recommend that the Board grant you an option (the “Option”) to purchase up to 40,000 shares of the Company’s Common Stock under the 2004 Equity Incentive Plan (the “Plan”) at an exercise price equal to the fair market value of the shares on the date of grant. We will provide your Option grant paperwork promptly after such grant has been made. Subject to the terms of the Plan and your related option agreement, your Option will vest as to 50% of the shares one year from the date referred to as the “Vesting Commencement Date”, and as to an additional 50% of the shares one year thereafter such that your Option will be fully vested on the two year anniversary of the Vesting Commencement Date.

In addition to the time-based vesting described in the preceding paragraph, if you are a Director of the Company on the date of a Change of Control (as defined below) that occurs before the two-year anniversary of the Vesting Commencement Date, in the event that a successor corporation refuses to assume or substitute the Option with an equivalent option or right, 100% of the shares subject to the Option shall immediately vest as of the effective date of such Change of Control. Notwithstanding any accelerated vesting contained in this paragraph, your total number of shares subject to the Option granted herein shall not increase by virtue of a Change of Control.

“Change of Control” means the occurrence of any of the following events:

(i) Any “person” (as such term is used in Sections 13(d) and 14(d) of the Exchange Act) becomes the “beneficial owner” (as defined in Rule 13d-3 of the Exchange Act), directly or indirectly, of securities of the Company representing fifty percent (50%) or more of the total voting power represented by the Company’s then outstanding voting securities; or

(ii) The consummation of the sale or disposition by the Company of all or substantially all of the Company’s assets;

6409 Guadalupe Mines Rd • San Jose, CA 95120 • U.S.A.

Tel: 408-826-0600 • Fax: 408-826-0601

www.monolithicpower.com

(iii) A change in the composition of the Board occurring within a two-year period, as a result of which fewer than a majority of the directors are Incumbent Directors. “Incumbent Directors” means directors who either (A) are Directors as of the effective date of the Plan, or (B) are elected, or nominated for election, to the Board with the affirmative votes of at least a majority of the Incumbent Directors at the time of such election or nomination (but will not include an individual whose election or nomination is in connection with an actual or threatened proxy contest relating to the election of directors to the Company); or

(iv) The consummation of a merger or consolidation of the Company with any other corporation, other than a merger or consolidation which would result in the voting securities of the Company outstanding immediately prior thereto continuing to represent (either by remaining outstanding or by being converted into voting securities of the surviving entity or its parent) at least fifty percent (50%) of the total voting power represented by the voting securities of the Company or such surviving entity or its parent outstanding immediately after such merger or consolidation.

Second, in addition to the indemnification rights you, in your capacity as a director of the Company, will be entitled to under the Company’s Bylaws and Certificate of Incorporation, we propose to grant you the additional contractual indemnification and related rights provided in the enclosed Indemnification Agreement.

Third, you will receive an annual retainer of $30,000 in connection with your seat on the Board and an annual retainer of $4,000 in connection with your participation on the Compensation Committee, subject to revision by the Board from time to time.

Fourth, the Company will reimburse you for international travel-related expenses associated with your attendance at Board of Directors meetings.

Finally, as you know, the Company’s intellectual property and other proprietary information is one of our most important assets and we must all be vigilant in our protection of it. Although it goes without saying, I feel it is appropriate to remind all new directors of their fiduciary duties of loyalty and care to the Company. These include the duty to maintain the confidentiality of the Company’s confidential and proprietary information and the duty to not use such information other than to promote the Company’s best interests. I am sure that you can appreciate the importance of these matters to us.

Again, I am happy to extend this invitation to you. Your participation on our Board would be of great benefit to the Company.

6409 Guadalupe Mines Rd • San Jose, CA 95120 • U.S.A.

Tel: 408-826-0600 • Fax: 408-826-0601

www.monolithicpower.com

6409 Guadalupe Mines Rd • San Jose, CA 95120 • U.S.A.

Tel: 408-826-0600 • Fax: 408-826-0601

www.monolithicpower.com