Other bills in the package include a requirement gun buyers pay the cost of their state background checks, background checks be conducted on all private gun sales and transfers, and a 15-round limit on magazines.
The bills go to the Senate for its consideration.
Proponents of the campus guns ban say campuses are generally safe and allowing guns would be counter-productive.
"There are a lot of students who simply are not ready to be in the presence of firearms," Rep. Claire Levy, D-Boulder, the bill's sponsor, said. "It's a dangerous mix."
Opponents counter allowing guns would mean college women would be better able to protect themselves from rapists and there would be a better chance someone bent on a mass shooting would be stopped, The Denver Post reported.
In 2003, the Legislature passed a law allowing individuals with a permit to carry a concealed weapon with a few exceptions, including K-12 schools but not colleges. Three University of Colorado students sued in 2008 and ultimately the state Supreme Court ruled administrators could not ban concealed weapons.