Preventing Gun Violence Act - Amends the federal criminal code to prohibit the trafficking in or possession of a firearm by a person who has been adjudicated to have committed a violent juvenile act. Defines "violent juvenile act" as an act by a person under the age of 18 that, if committed by an adult, would be punishable by a prison term exceeding one year and that: (1) has as an element the use, attempted use, or threatened use of physical force against another person; or (2) by its nature, involves a substantial risk that physical force against another person may be used in the course of committing the act.