Exhibit 4(h)


SUB-INVESTMENT ADVISORY AGREEMENT


AGREEMENT dated [_________], 2012, between
BlackRock Advisors, LLC, a Delaware limited liability company (the “Adviser”), and BlackRock (Singapore) Limited, a
corporation organized under the laws of Singapore (the “Sub-Adviser”).


WHEREAS, the Adviser has agreed to furnish
investment advisory services to the Funds listed on Appendix A (each, a “Fund”), each a series of BlackRock
Variable Series Funds, Inc., a Maryland corporation (the “Corporation”), an open-end management investment company
registered under the Investment Company Act of 1940, as amended (the “1940 Act”); and


WHEREAS, the Adviser wishes to retain
the Sub-Adviser to provide it with certain sub-advisory services as described below in connection with Adviser’s advisory
activities on behalf of the Funds; and


WHEREAS, the advisory agreement between
the Adviser and the Corporation, dated September 29, 2006 and Amendment No. 1 thereto, dated June 1, 2011 (such agreement or the
most recent successor agreement between such parties relating to advisory services to the Corporation is referred to herein as
the “Advisory Agreement”) contemplates that the Adviser may sub-contract investment advisory services with respect
to the Funds to a sub-adviser pursuant to a sub-advisory agreement agreeable to the Corporation and approved in accordance with
the provisions of the 1940 Act; and


WHEREAS, this Agreement has been approved
in accordance with the provisions of the 1940 Act, and the Sub-Adviser is willing to furnish such services upon the terms and conditions
herein set forth.


NOW, THEREFORE, in consideration of the
mutual premises and covenants herein contained and other good and valuable consideration, the receipt of which is hereby acknowledged,
it is agreed by and between the parties hereto as follows:


1.                 
Appointment. The Adviser hereby appoints the Sub-Adviser to act as sub-adviser with respect to the Funds and the
Sub-Adviser accepts such appointment and agrees to render the services herein set forth for the compensation herein provided.


2.                 
Services of the Sub-Adviser. Subject to the succeeding provisions of this section, the oversight and supervision
of the Adviser and the direction and control of the Corporation’s Board of Directors, the Sub-Adviser will perform certain
of the day-to-day operations of the Funds, which may include one or more of the following services, at the request of the Adviser
: (a) acting as investment adviser for and managing the investment and reinvestment of those assets of the Funds as the Adviser
may from time to time request and in connection therewith have complete discretion in purchasing and selling such securities and
other assets for the Funds and in voting, exercising consents and exercising all other rights appertaining to such securities and
other assets on behalf of the Funds; (b) arranging, subject to the provisions of paragraph 3 hereof, for the purchase and sale
of securities and other assets of the Funds; (c) providing investment research and credit analysis concerning the Funds’
investments, (d) assisting the Adviser in determining what portion of the Funds’ assets will be invested in cash, cash equivalents
and money market instruments, (e) placing orders for all purchases and sales of such




    	 



    	 



    



investments made for the Funds,
and (f) maintaining the books and records as are required to support Fund investment operations. At the request of the Adviser
, the Sub-Adviser will also, subject to the oversight and supervision of the Adviser and the direction and control of the Corporation’s
Board of Directors, provide to the Adviser or the Funds any of the facilities and equipment and perform any of the services described
in Section 3 of the Advisory Agreement. In addition, the Sub-Adviser will keep the Funds and the Adviser informed of developments
materially affecting the Funds and shall, on its own initiative, furnish to the Funds from time to time whatever information the
Sub-Adviser believes appropriate for this purpose. The Sub-Adviser will periodically communicate to the Adviser , at such times
as the Adviser may direct, information concerning the purchase and sale of securities for the Funds, including: (a) the name of
the issuer, (b) the amount of the purchase or sale, (c) the name of the broker or dealer, if any, through which the purchase or
sale is effected, (d) the CUSIP number of the instrument, if any, and (e) such other information as the Adviser may reasonably
require for purposes of fulfilling its obligations to the Funds under the Advisory Agreement. The Sub-Adviser will provide the
services rendered by it under this Agreement in accordance with each Fund’s investment objectives, policies and restrictions
(as currently in effect and as they may be amended or supplemented from time to time) as stated in the Funds’ Prospectus
and Statement of Additional Information and the resolutions of the Corporation’s Board of Directors.


3.                 
Covenants.


(a)               
In the performance of its duties under this Agreement, the Sub-Adviser shall at all times conform to, and act in accordance
with, any requirements imposed by: (i) the provisions of the 1940 Act and the Investment Advisers Act of 1940, as amended (the
“Advisers Act”) and all applicable Rules and Regulations of the Securities and Exchange Commission (the “SEC”);
(ii) any other applicable provision of law; (iii) the provisions of the Agreement and Charter and By-Laws of the Corporation, as
such documents are amended from time to time; (iv) the investment objectives and policies of the Funds as set forth in its Registration
Statement on Form N-1A and/or the resolutions of the Board of Directors; and (v) any policies and determinations of the Board
of Directors of the Corporation and


(b)              
In addition, the Sub-Adviser will:


(i)                
place orders either directly with the issuer or with any broker or dealer. Subject to the other provisions of this paragraph,
in placing orders with brokers and dealers, the Sub-Adviser will attempt to obtain the best price and the most favorable execution
of its orders. In placing orders, the Sub-Adviser will consider the experience and skill of the firm’s securities traders
as well as the firm’s financial responsibility and administrative efficiency. Consistent with this obligation, the Sub-Adviser
may select brokers on the basis of the research, statistical and pricing services they provide to the Funds and other clients of
the Adviser or the Sub-Adviser. Information and research received from such brokers will be in addition to, and not in lieu of,
the services required to be performed by the Sub-Adviser hereunder. A commission paid to such brokers may be higher than that which
another qualified broker would have charged for effecting the same transaction, provided that the Sub-Adviser determines in good
faith that such commission is reasonable in terms either of the transaction or the overall responsibility of the Adviser and the
Sub-Adviser to the Funds and their other clients and that the total




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commissions paid by each Fund
will be reasonable in relation to the benefits to the Fund over the long-term. Subject to the foregoing
and the provisions of the 1940 Act, the Securities Exchange Act of 1934, as amended, and other applicable provisions of law, the
Sub-Adviser may select brokers and dealers with which it or the Corporation is affiliated;


(ii)              
maintain books and records with respect to the Funds’ securities transactions and will render to the Adviser and the
Corporation’s Board of Directors such periodic and special reports as they may request;


(iii)            
maintain a policy and practice of conducting its investment advisory services hereunder independently of the commercial
banking operations of its affiliates. When the Sub-Adviser makes investment recommendations for the Funds, its investment advisory
personnel will not inquire or take into consideration whether the issuer of securities proposed for purchase or sale for each Fund’s
account are customers of the commercial department of its affiliates; and


(iv)            
treat confidentially and as proprietary information of the Funds all records and other information relative to the Funds,
and the Funds’ prior, current or potential shareholders, and will not use such records and information for any purpose other
than performance of its responsibilities and duties hereunder, except after prior notification to and approval in writing by each
Fund, which approval shall not be unreasonably withheld and may not be withheld where the Sub-Adviser may be exposed to civil or
criminal contempt proceedings for failure to comply, when requested to divulge such information by duly constituted authorities,
or when so requested by the Funds.


4.                 
Services Not Exclusive. Nothing in this Agreement shall prevent the Sub-Adviser or any officer, employee or other
affiliate thereof from acting as investment adviser for any other person, firm or corporation, or from engaging in any other lawful
activity, and shall not in any way limit or restrict the Sub-Adviser or any of its officers, employees or agents from buying, selling
or trading any securities for its or their own accounts or for the accounts of others for whom it or they may be acting; provided,
however, that the Sub-Adviser will undertake no activities which, in its judgment, will adversely affect the performance of its
obligations under this Agreement.


5.                 
Books and Records. In compliance with the requirements of Rule 31a-3 under the 1940 Act, the Sub-Adviser hereby agrees
that all records which it maintains for the Corporation are the property of the Corporation and
further agrees to surrender promptly to the Corporation any such records upon the Corporation’s
request. The Sub-Adviser further agrees to preserve for the periods prescribed by Rule 31a-2 under the 1940 Act the records required
to be maintained by Rule 31a-1 under the 1940 Act (to the extent such books and records are not maintained by the Adviser).


6.                 
Expenses. During the term of this Agreement, the Sub-Adviser will bear all costs and expenses of its employees and
any overhead incurred by the Sub-Adviser in connection with its duties hereunder; provided that the Board of Directors of the Corporation
may approve reimbursement to the Sub-Adviser of the pro-rata portion of the salaries, bonuses, health




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insurance, retirement benefits and
all similar employment costs for the time spent on Fund operations (including, without limitation, compliance matters) (other than
the provision of investment advice and administrative services required to be provided hereunder) of all personnel employed by
the Sub-Adviser who devote substantial time to Fund operations or the operations of other investment companies advised or sub-advised
by the Sub-Adviser.


7.                 
Compensation.


(a)               
The Adviser agrees to pay to the Sub-Adviser and the Sub-Adviser agrees to accept as full compensation for all services
rendered by the Sub-Adviser as such, a monthly fee in arrears at an annual rate equal to the amount set forth in Schedule A hereto.
For any period less than a month during which this Agreement is in effect, the fee shall be prorated according to the proportion
which such period bears to a full month of 28, 29, 30 or 31 days, as the case may be.


(b)              
For purposes of this Agreement, the net assets of the Funds shall be calculated pursuant to the procedures adopted by resolutions
of the Directors of the Corporation for calculating the value of each Fund’s assets or delegating such calculations to third
parties.


8.                 
Indemnity.


(a)               
The Funds hereby agree to indemnify the Sub-Adviser, and each of the Sub-Adviser’s directors, officers, employees,
agents, associates and controlling persons and the directors, partners, members, officers, employees and agents thereof (including
any individual who serves at the Sub-Adviser’s request as director, officer, partner, member, trustee or the like of another
entity) (each such person being an “Indemnitee”) against any liabilities and expenses, including amounts paid in satisfaction
of judgments, in compromise or as fines and penalties, and counsel fees (all as provided in accordance with applicable state law)
reasonably incurred by such Indemnitee in connection with the defense or disposition of any action, suit or other proceeding, whether
civil or criminal, before any court or administrative or investigative body in which such Indemnitee may be or may have been involved
as a party or otherwise or with which such Indemnitee may be or may have been threatened, while acting in any capacity set forth
herein or thereafter by reason of such Indemnitee having acted in any such capacity, except with respect to any matter as to which
such Indemnitee shall have been adjudicated not to have acted in good faith in the reasonable belief that such Indemnitee’s
action was in the best interest of the Corporation and furthermore, in the case of any criminal proceeding, so long as such Indemnitee
had no reasonable cause to believe that the conduct was unlawful; provided, however, that (1) no Indemnitee shall be indemnified
hereunder against any liability to the Corporation or a Fund or its shareholders or any expense of such Indemnitee arising by reason
of (i) willful misfeasance, (ii) bad faith, (iii) gross negligence or (iv) reckless disregard of the duties involved in the conduct
of such Indemnitee’s position (the conduct referred to in such clauses (i) through (iv) being sometimes referred to herein
as “disabling conduct”), (2) as to any matter disposed of by settlement or a compromise payment by such Indemnitee,
pursuant to a consent decree or otherwise, no indemnification either for said payment or for any other expenses shall be provided
unless there has been a determination that such settlement or compromise is in the best interests of a Fund and that such Indemnitee
appears to have acted in good faith in the reasonable belief that such Indemnitee’s action was in the best interest of a
Fund and did not involve disabling




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conduct by such Indemnitee and (3)
with respect to any action, suit or other proceeding voluntarily prosecuted by any Indemnitee as plaintiff, indemnification shall
be mandatory only if the prosecution of such action, suit or other proceeding by such Indemnitee was authorized by a majority of
the full Board of Directors of the Corporation.


(b)              
The Funds shall make advance payments in connection with the expenses of defending any action with respect to which indemnification
might be sought hereunder if the Corporation receives a written affirmation of the Indemnitee’s good faith belief that the
standard of conduct necessary for indemnification has been met and a written undertaking to reimburse a Fund unless it is subsequently
determined that such Indemnitee is entitled to such indemnification and if the Directors of the Corporation determine that the
facts then known to them would not preclude indemnification. In addition, at least one of the following conditions must be met:
(A) the Indemnitee shall provide a security for such Indemnitee’s undertaking, (B) the Corporation shall be insured against
losses arising by reason of any unlawful advance, or (C) a majority of a quorum consisting of Directors of the Corporation who
are neither “interested persons” of the Corporation (as defined in Section 2(a)(19) of the 1940 Act) nor parties to
the proceeding (“Disinterested Non-Party Directors”) or an independent legal counsel in a written opinion, shall determine,
based on a review of readily available facts (as opposed to a full trial-type inquiry), that there is reason to believe that the
Indemnitee ultimately will be found entitled to indemnification.


(c)               
All determinations with respect to the standards for indemnification hereunder shall be made (1) by a final decision on
the merits by a court or other body before whom the proceeding was brought that such Indemnitee is not liable by reason of disabling
conduct, or (2) in the absence of such a decision, by (i) a majority vote of a quorum of the Disinterested Non-Party Directors
of the Corporation, or (ii) if such a quorum is not obtainable or even, if obtainable, if a majority vote of such quorum so directs,
independent legal counsel in a written opinion. All determinations that advance payments in connection with the expense of defending
any proceeding shall be authorized shall be made in accordance with the immediately preceding clause (2) above.


The rights accruing to any Indemnitee
under these provisions shall not exclude any other right to which such Indemnitee may be lawfully entitled.


9.                 
Limitation on Liability. The Sub-Adviser will not be liable for any error of judgment or mistake of law or for any
loss suffered by the Adviser or by the Fund in connection with the performance of this Agreement, except a loss resulting from
a breach of fiduciary duty with respect to the receipt of compensation for services or a loss resulting from willful misfeasance,
bad faith or gross negligence on its part in the performance of its duties or from reckless disregard by it of its duties under
this Agreement.


10.             
Duration and Termination. This Agreement shall become effective as of the date hereof and, unless sooner terminated
with respect to the Funds as provided herein, shall continue in effect for a period of two years. Thereafter, if not terminated,
this Agreement shall continue in effect with respect to the Funds for successive periods of 12 months, provided such continuance
is specifically approved at least annually by both (a) the vote of a majority of the Corporation’s Board of Directors or
a vote of a majority of the outstanding voting securities of each Fund at the




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time outstanding and entitled to
vote and (b) by the vote of a majority of the Directors, who are not parties to this Agreement or interested persons (as such term
is defined in the 1940 Act) of any such party, cast in person at a meeting called for the purpose of voting on such approval. Notwithstanding
the foregoing, this Agreement may be terminated by the Corporation or the Adviser at any time, without the payment of any penalty,
upon giving the Sub-Adviser 60 days’ notice (which notice may be waived by the Sub-Adviser), provided that such termination
by the Corporation, on behalf of a Fund, or the Adviser shall be directed or approved by the vote of a majority of the Directors
of the Corporation in office at the time or by the vote of the holders of a majority of the outstanding voting securities of each
Fund entitled to vote, or by the Sub-Adviser on 60 days’ written notice (which notice may be waived by the Corporation, on
behalf of a Fund, and the Adviser), and will terminate automatically upon any termination of the Advisory Agreement between the
Corporation and the Adviser. This Agreement will also immediately terminate in the event of its assignment. (As used in this Agreement,
the terms “majority of the outstanding voting securities,” “interested person” and “assignment”
shall have the same meanings of such terms in the 1940 Act.)


11.             
Notices. Any notice under this Agreement shall be in writing to the other party at such address as the other party
may designate from time to time for the receipt of such notice and shall be deemed to be received on the earlier of the date actually
received or on the fourth day after the postmark if such notice is mailed first class postage prepaid.


12.             
Amendment of this Agreement. This Agreement may be amended by the parties only if such amendment is specifically
approved by the vote of the Board of Directors of the Corporation, including a majority of those Directors who are not parties
to this Agreement or interested persons of any such party cast in person at a meeting called for the purpose of voting on such
approval and, where required by the 1940 Act, by a vote of a majority of the outstanding voting securities of each Fund.


13.             
Miscellaneous. The captions in this Agreement are included for convenience of reference only and in no way define
or delimit any of the provisions hereof or otherwise affect their construction or effect. If any provision of this Agreement shall
be held or made invalid by a court decision, statute, rule or otherwise, the remainder of this Agreement shall not be affected
thereby. This Agreement shall be binding on, and shall inure to the benefit of the parties hereto and their respective successors.


14.             
Governing Law. This Agreement shall be governed by and construed in accordance with the laws of the State of New
York for contracts to be performed entirely therein without reference to choice of law principles thereof and in accordance with
the applicable provisions of the 1940 Act. To the extent that the applicable laws of the State of New York, or any of the provisions,
conflict with the applicable provisions of the 1940 Act, the latter shall control.


15.             
Counterparts. This Agreement may be executed in counterparts by the parties hereto, each of which shall constitute
an original counterpart, and all of which, together, shall constitute one Agreement.




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IN WITNESS WHEREOF, the parties hereto
have caused this instrument to be executed by their duly authorized officers designated below as of the day and year first above
written.


 


BLACKROCK ADVISORS, LLC


 


 


By:                                                                 


Name:


Title:


 


 


BLACKROCK (HONG KONG) LIMITED


 


 


By:                                                                 


Name:


Title:


 


 


AGREED AND ACCEPTED

as of the date first set forth above


BLACKROCK VARIABLE SERIES FUNDS, INC.


By:                                                              


Name:

Title:




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Appendix A


 


	
        Name of Series 
	
        Effective Date

	BlackRock Managed Volatility V.I. Fund	[____ __], 2012


 




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Schedule A


Sub-Investment Advisory Fee


BlackRock Managed Volatility V.I. Fund


Pursuant to Section 7, for that portion of BlackRock Managed
Volatility V.I. Fund for which the Sub-Adviser acts as sub-adviser, Adviser shall pay a fee to Sub-Adviser equal to [____] percent
([__]%) of the advisory fee received by the Adviser from the Fund with respect to such portion, net of: (i) expense waivers and
reimbursements, (ii) expenses relating to distribution and sales support activities borne by the Adviser, and (iii) administrative,
networking, recordkeeping, sub-transfer agency and shareholder services expenses borne by the Adviser.




 






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