Gun Show Background Check Act of 2001

Provides that if any part of a firearm transaction takes place at a gun show, each licensed importer, manufacturer, and dealer who transfers one or more firearms to a person who is not licensed shall, within ten days after the transfer, submit a report of the transfer to the Secretary of the Treasurer. Sets forth penalties for violations.

Grants the Secretary authority to enter the place of business of any gun show promoter and any place where a gun show is held, during business hours and without a showing of reasonable cause or a warrant, for purposes of examining records and the inventory of licensees conducting business to determine compliance with this Act.

Increases penalties for: (1) serious record-keeping violations by licensees; and (2) violations of criminal background check requirements.

Modifies provisions regarding the national instant criminal background check system and the destruction of records in cases where receipt of a firearm would not violate the Brady Act or State law to provide for such destruction as soon as possible, consistent with the Attorney General's responsibility to ensure privacy and security of the system and to prevent system fraud and abuse, but in no event later than 90 days after the licensee first contacts the system.