Exhibit 2

Execution Version

Stifel Venture Corp

237 Park Avenue

8th Floor

New York, New York 10022

January 2, 2014

Raymond James & Associates, Inc.

As Representative of the several Underwriters

named in Schedule A to the Underwriting Agreement

c/o Raymond James & Associates, Inc.

50 North Front Street, 17th Floor

Memphis, Tennessee 38103

Re:  Lock-Up Agreement for shares of CM Finance Inc

Ladies & Gentlemen:

The undersigned is an officer, director and/or owner of record or beneficially of shares of common stock (“Common Stock”) of CM Finance Inc, a Maryland corporation (the “Company”).  The Company proposes to carry out a public offering of Common Stock (the “Offering”)for which you will act as the representative (the “Representative”) of the several underwriters (the “Underwriters”) listed on Schedule A to the underwriting agreement (the “Underwriting Agreement”) by and among the Company, CM Investment Partners LLC, and the Underwriters.  The undersigned recognizes that the Offering will be of benefit to the undersigned and will benefit the Company by, among other things, raising additional capital for its operations.  The undersigned acknowledges that you are relying on the representations and agreements of the undersigned contained in this letter agreement (this “Agreement”) in carrying out the Offering and in entering into the Underwriting Agreement with the Company with respect to the Offering.

In consideration of the foregoing, the undersigned hereby agrees that the undersigned, for a period commencing on the date hereof and continuing through the close of trading on the date 365 days after the public offering date set forth on the final prospectus used to sell the Common Stock in the Offering (the “Lock-up Period”) pursuant to the Underwriting Agreement, will not (and will cause any spouse or immediate family member of the spouse or the undersigned living in the undersigned’s household and any trustee of any trust that holds Common Stock for the benefit of the undersigned or such spouse or family member not to), without the prior written consent of the Representative on behalf of the Underwriters (which consent may be withheld in their sole discretion), directly or indirectly, (1) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase or otherwise transfer or dispose of (or enter into any transaction or device that is designed to, or could be expected to, result in the disposition by any person at any time in the future of) any Common Stock (including, without limitation, shares of Common Stock that may be deemed to be beneficially owned by the undersigned in accordance with the rules and

regulations of the Securities and Exchange Commission), (2) enter into any swap or other derivatives transaction that transfers to another, in whole or in part, any economic benefits or risks of ownership of shares of the Common Stock, whether any such transaction described in clause (1) or (2) above is to be settled by delivery of the Common Stock, in cash or otherwise, or (3) publicly announce an intention to do any of the foregoing.

The foregoing restrictions have been expressly agreed to by the undersigned so as to preclude the undersigned (or such spouse, family member or trustee) from engaging in any hedging or other transaction that is designed to or reasonably expected to lead to or result in a disposition of shares of Common Stock during the Lock-up Period, even if such Common Stock would be disposed of by someone other than such holder.  Such prohibited hedging or other transactions would include, without limitation, any short sale (whether or not against the box) or any purchase, sale or grant of any right (including, without limitation, any put or call option) with respect to any security (other than a broad-based market basket or index) that includes, relates to or derives any significant part of its value from the Common Stock.  In addition, the undersigned agrees that, without the prior written consent of the Representative on behalf of the Underwriters, it will not, during the Lock-Up Period, make any demand for or exercise any right with respect to, the registration of any Common Stock or any security convertible into or exercisable or exchangeable for the Common Stock.

If the undersigned is an officer or director of the Company, the undersigned further agrees that the foregoing provisions shall be equally applicable to any Company-directed Common Stock the undersigned may purchase or otherwise receive in the Offering (including pursuant to a Directed Share Program).

The foregoing shall not apply to the following:  (1) the registration of or sale to the Underwriters of Common Stock pursuant to the Offering and the Underwriting Agreement, (2) the issuance of shares of Common Stock in connection with the Formation Transactions (as defined in the Underwriting Agreement), (3) the issuance of shares of Common Stock issuable under the Company’s dividend reinvestment plan, (4) bona fide gifts, succession and inheritance by will or intestacy, (5) transfers to trusts for the benefit of the undersigned, any spouse, immediate family member or a charitable, educational or religious institution by the undersigned; provided, however, that in the case of a transfer under clause (4) or (5), the transferee(s)/donee(s) shall agree in writing prior to such disposition to be bound by the restrictions set forth herein and to the extent any interest in the Common Stock is retained by the undersigned (or such spouse or family member), the Common Stock shall remain subject to the restrictions contained in this Agreement.  For the avoidance of doubt, the foregoing restrictions are not meant to, and shall not, apply to any affiliates of the undersigned, including, without limitation with respect to any market-making activities conducted by such affiliates.

The undersigned also agrees and consents (1) with respect to Common Stock held of record by the undersigned, to the entry of stop transfer instructions with the Company’s transfer agent and registrar against the transfer of such Common Stock as described herein except in compliance with this Agreement, and (2) with respect to Common Stock beneficially owned, but not held of record by, the undersigned, to cause the record holder of such Common Stock to agree and consent to the entry of stop transfer instructions with the Company’s transfer agent and

registrar against the transfer of such Common Stock as described herein except in compliance with this Agreement.

If the undersigned is an officer or director of the Company, the Representative agrees that, at least three business days prior to the release or waiver of any of the foregoing restrictions with respect to the Common Stock of the undersigned, including, for the avoidance of doubt, any security of the Company acquired by the undersigned from the Company in the Offering, the Representative will (i) notify the Company of the impending release or waiver and (ii) announce such impending release or waiver through a major news service in the event that the Company fails to make such announcement in accordance with its obligations under the Underwriting Agreement; provided, however, that nowhere the release or waiver is effected solely to permit a transfer of securities that is not for consideration and where the transferee has agreed in writing to be bound by the terms of this Agreement.  Any such release or waiver granted hereunder shall only be effective two business days after such announcement is made by the Company or the Representative.  The provisions of this paragraph shall not apply to any release or waiver granted solely to permit a transfer of securities that is not for consideration and where the transferee has agreed in writing to be bound by the terms of this Agreement.

It is understood that, if (1) the Company notifies the undersigned that it does not intend to proceed with the Offering, (2) the registration statement filed with the Securities and Exchange Commission with respect to the Offering is withdrawn, or (3) for any reason the Underwriting Agreement shall terminate or be terminated prior to payment for and delivery of the Common Stock to be sold thereunder, the undersigned will be released from its obligations under this Agreement.

[Signature Page Follows]

This Agreement is irrevocable and will be binding on the undersigned and the respective successors, heirs, personal representatives and assigns of the undersigned.

Very truly yours,

STIFEL VENTURE CORP.

                                                                                                 /s/ Bernard N. Burkemper

                                                                                                Name:  Bernard N. Burkemper

                                                                                                Title:    Vice President, Stifel Venture Corp.

                                                                                               [Signature Page- Lock-Up Agreement]