Child Gun Safety and Gun Access Prevention Act of 2013

Child Gun Safety and Gun Access Prevention Act of 2013 - Amends the Brady Handgun Violence Prevention Act to: (1) raise the age of handgun eligibility to 21 (currently, 18); and (2) prohibit persons under age 21 from possessing semiautomatic assault weapons or large capacity ammunition feeding devices, with exceptions.

Increases penalties for: (1) a second or subsequent violation by a juvenile of Brady Act provisions or for a first violation committed after an adjudication of delinquency or after a state or federal conviction for an act that, if committed by an adult, would be a serious violent felony; and (2) transferring a handgun, ammunition, semiautomatic assault weapon, or large capacity ammunition feeding device to a person who is under age 21, knowing or having reasonable cause to know that such person intended to use it in the commission of a crime of violence.

Prohibits any licensed importer, manufacturer, or dealer from transferring a firearm to any person (other than a licensed importer, manufacturer, or dealer) unless the transferee is provided with a secure gun storage or safety device. Authorizes the Attorney General to suspend or revoke any firearms license, or to subject the licensee to a civil penalty of up to $10,000, if the licensee has knowingly violated this prohibition.

Prohibits keeping a loaded firearm or an unloaded firearm and ammunition within any premises knowing or recklessly disregarding the risk that a child: (1) is capable of gaining access to it, and (2) will use the firearm to cause death or serious bodily injury.

Requires the parent or legal guardian of a child to ensure that a child attending a gun show is accompanied by an adult.

Authorizes the Attorney General to provide grants to enable local law enforcement agencies to develop and sponsor gun safety classes for parents and children.

Expresses the sense of Congress that each school district should provide or participate in a firearms safety program for students.