Gun Show Loophole Closing Act of 2003 - Amends the Brady Handgun Violence Prevention Act to provide for regulation of firearms transfers at special firearms events (events at which 75 or more firearms are offered or exhibited for sale, exchange, or transfer if one or more of the firearms has been shipped or transported in, or otherwise affects, interstate or foreign commerce, excluding an offer or exhibit of firearms: (1) by an individual, from that individual's personal collection, at that individual's private residence, if the individual is not required to be licensed; and (2) at events conducted and attended by permanent or annual dues paying members of private, not-for-profit organizations whose primary purpose is owning and maintaining real property for hunting activities).

Prohibits any person from operating a special firearms event without notifying the Attorney General. Sets forth: (1) responsibilities of special firearms events operators and of firearms licensees and transferors other than licensees at such events, including with regard to criminal background checks; (2) special firearms event license application requirements; and (3) penalties for violation of this Act.

Authorizes a State to apply to the Attorney General for, and sets forth criteria for, certification of the 24-hour verification authority of that State with respect to criminal background checks.

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