The National Right-to-Carry Reciprocity Act of 2011 passed 272-154 with 229 Republicans and 43 Democrats backing it, the Los Angeles Times said.
Proponents want the measure to make it easier for gun owners to travel between states without having to worry whether their permit is valid, but opponents view it as a federal infringement on states' rights, the newspaper said.
"The simple right to defend yourself and loved ones from criminals is fundamental, and it doesn't extinguish when you cross a state border," said Rep. Cliff Stearns, R-Fla., who sponsored the bill.
The bill goes to the Senate where similar legislation died in 2009.
Forty states have some form of concealed-weapon-permit reciprocity, advocates said.