NPI Nuveen Premium Income Municipal Fund, Inc.

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13G

Under the Securities Exchange Act of 1934

(Amendment No.    )*

Nuveen Premium Income Municipal Fund, Inc.

(Name of Issuer)

Variable Rate MuniFund Term Preferred Shares Series 2015

(Title of Class of Securities)

67062T886

(CUSIP Number)

November 1, 2012

(Date of Event Which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to which this Schedule is filed:

x  Rule 13d-1(b)

¨  Rule 13d-1(c)

¨  Rule 13d-1(d)

The information required in the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

Item 1(a) Name of issuer:

Nuveen Premium Income Municipal Fund, Inc.

Item 1(b) Address of issuer’s principal executive offices:

333 West Wacker Drive

Chicago, Illinois 60606

2(a) Name of person filing:

Wells Fargo Bank, National Association

2(b) Address or principal business office or, if none, residence:

101 N. Phillips Avenue

Sioux Falls, South Dakota 57104

2(c) Citizenship:

United States of America

2(d) Title of class of securities:

Variable Rate MuniFund Term Preferred Shares Series 2015 (“VMTP”)

2(e) CUSIP No.:

67062T886

Item 3. If this statement is filed pursuant to §§240.13d–1(b) or 240.13d–2(b) or (c), check whether the person filing is a:

(a) ¨ Broker or dealer registered under section 15 of the Act (15 U.S.C. 78o);

(b) x Bank as defined in section 3(a)(6) of the Act (15 U.S.C. 78c);

(c) ¨ Insurance company as defined in section 3(a)(19) of the Act (15 U.S.C. 78c);

(d) ¨ Investment company registered under section 8 of the Investment Company Act of 1940 (15 U.S.C 80a–8);

(e) ¨ An investment adviser in accordance with §240.13d–1(b)(1)(ii)(E);

(f) ¨ An employee benefit plan or endowment fund in accordance with §240.13d–1(b)(1)(ii)(F);

(g) ¨ A parent holding company or control person in accordance with §240.13d–1(b)(1)(ii)(G);

(h) ¨ A savings associations as defined in Section 3(b) of the Federal Deposit Insurance Act (12 U.S.C. 1813);

(i) ¨ A church plan that is excluded from the definition of an investment company under section 3(c)(14) of the Investment Company Act of 1940 (15 U.S.C. 80a–3);

(j) ¨ A non-U.S. institution in accordance with §240.13d–1(b)(1)(ii)(J);

(k) ¨ Group, in accordance with §240.13d–1(b)(1)(ii)(K). If filing as a non-U.S. institution in accordance with §240.13d–1(b)(1)(ii)(J), please specify the type of institution:             

Item 4. Ownership

Provide the following information regarding the aggregate number and percentage of the class of securities of the issuer identified in Item 1.

(a) Amount beneficially owned: 4,070

(b) Percent of class: 100%.

(c) Number of shares as to which the person has:

(i) Sole power to vote or to direct the vote: 4,070

(ii) Shared power to vote or to direct the vote: 0

(iii) Sole power to dispose or to direct the disposition of: 4,070

(iv) Shared power to dispose or to direct the disposition of: 0

Item 5. Ownership of 5 Percent or Less of a Class.

If this statement is being filed to report the fact that as of the date hereof the reporting person has ceased to be the beneficial owner of more than 5 percent of the class of securities, check the following   ¨ .

Item 6. Ownership of More than 5 Percent on Behalf of Another Person.

Not Applicable

Item 7. Identification and Classification of the Subsidiary Which Acquired the Security Being Reported on by the Parent Holding Company or Control Person.

Not Applicable

Item 8. Identification and Classification of Members of the Group

Not Applicable

Item 9. Notice of Dissolution of Group.

Not Applicable

Item 10. Certifications

By signing below I certify that, to the best of my knowledge and belief, the securities referred to above were acquired and are held in the ordinary course of business and were not acquired and are not held for the purpose of or with the effect of changing or influencing the control of the issuer of the securities and were not acquired and are not held in connection with or as a participant in any transaction having that purpose or effect.

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

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