Heller Public Firearms Range Act of 2014 - Amends the Pittman-Robertson Wildlife Restoration Act to include the District of Columbia in the apportionment to states and U.S. territories and possessions of revenues from taxes imposed on pistols, revolvers, bows, and arrows.

Revises specified payments authority to: (1) authorize the Secretary of the Interior to cooperate with the Mayor of the District in conducting wildlife restoration projects and hunter safety programs; (2) authorize payments to the District out of funds made available under the Act for such purposes; and (3) limit the amount of such payments to one-half of 1% of the total amount apportioned to states, territories, and possessions for any year.

Requires the Secretary to use amounts in the federal aid to wildlife restoration fund (FAWRF) to make a limited grant in FY2015 to the Mayor for construction and operation of an indoor public target range for firearm users in the District.

Requires the Secretary to construct and operate the target range on suitable federal land within the District using FAWRF funds and such grant amount or from other sources, if the Mayor fails to apply for the grant within 90 days after enactment of this Act or fails to construct a target range with it within one year after the enactment.