Renovate and Enhance Veterans' Meeting Halls and Posts Act of 2015 or REVAMP Act of 2015

Amends the Housing and Community Development Act of 1974 to require the Department of Housing and Urban Development to make competitive grants to eligible veterans service organizations for: (1) repairs or rehabilitation of their existing facilities, and (2) acquiring or upgrading computers and technology for such facilities.

Defines "eligible veterans service organization" as: (1) a tax-exempt entity organized on a local or area basis; and (2) a tax-exempt local or area chapter, post, or other unit of a national, regional, statewide, or other larger entity of which local or area chapters, posts, or units are members (but not any such national, regional, statewide, or other larger entity itself).

Prohibits an eligible veterans service organization from receiving such grant amounts, for any single fiscal year, in an amount exceeding the lesser of: (1) the aggregate cost of the proposed activities and uses for which the grant amounts will be used, or (2) $200,000.

Makes a grant recipient ineligible to receive another such grant for any of the five succeeding fiscal years.

Prohibits the use of such grants for construction or acquisition of a new facility.