Using someone able to buy a gun to give it to someone who isn't allowed to have a gun is called a "straw purchase."
The vote was 11-7 on the Senate Judiciary Committee, with Sen. Charles Grassley of Iowa being the only Republican to vote for the proposal, The New York Times reported. The panel is made up of 10 Democrats and eight Republicans.
The bill now goes to the full Senate.
The Times said several Republicans spoke out against the proposal, including Sen. John Cornyn of Texas. Cornyn said the bill would be used "to show we are doing something," but would not halt gun crimes.
The committee is expected to vote on three other gun control proposals, including an assault weapons ban from Sen. Dianne Feinstein, D-Calif.
Feinstein said despite support for the ban from law enforcement, medical and other groups, "it's as if we have a minority insubstantial piece of legislation."
The Times said if Congress fails to pass more than a modified straw purchasing bill, it would be a victory for the National Rifle Association, which opposes each measure.