UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 or 15(d)

of the Securities Exchange Act of 1934

Date of Report (Date of earliest event reported): August 5, 2016

Nuveen Maryland Premium Income Municipal Fund

(Exact name of registrant as specified in its charter)

Registrant’s telephone number, including area code: (800) 257-8787

(Former name or former address, if changed since last report)

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions:

Investment Policy Revision

Effective August 5, 2016, a number of Nuveen AMT-Free and non-AMT municipal closed-end funds have approved changes to their investment policies altering the limits on exposure to securities subject to the federal alternative minimum tax applicable to individuals (AMT).

AMT FREE MUNICIPAL FUNDS

The two AMT-Free funds listed below adopted a new investment policy to require the funds to invest 100% of its managed assets in securities the income from which is exempt from AMT at the time of purchase. While the funds were previously being managed as such, the new AMT policy will be in addition to the current policy which requires that only 80% of the funds’ assets be invested in securities exempt from the AMT. The 80% policy was adopted to meet the “Names Rule” under the Investment Company Act of 1940 and is subject to change by the board upon 60 days’ notice to shareholders. The new 100% AMT policy is subject to change by the fund’s board without shareholder notice. The new AMT policy is consistent with Nuveen’s other AMT-Free funds. The new policy was adopted for the following funds:

MUNICIPAL FUNDS THAT ARE NOT AMT-FREE

All of the Nuveen municipal closed-end funds listed below have adopted an investment policy to limit the amount securities subject to AMT to no more than 20% of a fund’s managed assets. As set forth below the vast majority of these funds previously did not have a limit on AMT securities while six funds had a 30% limit on AMT securities. The new AMT investment policy will replace each fund’s old investment policy. Together with a number of other Nuveen funds, these changes will create a uniform 20% limit on AMT securities across Nuveen’s municipal complex. The following is a list of the funds adopting the new 20% limit and each fund’s previous investment policy with respect to AMT securities.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.