Gun Crime Prosecution Act of 2001 - Requires the U.S. Attorney for each judicial district to: (1) appoint one additional Assistant U.S. Attorney for that district to be responsible for prosecuting only offenses under Federal law involving firearms or ammunition; and (2) require such Assistant Attorney to give priority to crimes of violence committed by individuals who have previously been convicted of such a crime and to offenses by individuals who have previously been convicted of a crime punishable by imprisonment for more than one year.