The bill would remove marijuana from the Controlled Substances Act and permit states to make their own rules on the drug, the Associated Press reported.
It would also levy a 5% sales tax on marijuana products and would require federal courts to erase prior marijuana convictions.
Many Americans live in states where marijuana is legal in some form and federal policy on the drug has lagged behind states, committee members noted.
The vote supporting the bill "marks a turning point for federal cannabis policy and is truly a sign that prohibition's days are numbered," Aaron Smith, executive director of the National Cannabis Industry Association, said in a statement, the AP reported.
But it wasn't immediately clear if the proposal would be reviewed by other committees and when, or if, a vote would take place in the full House. The proposal has better chances of passing in the Democratic-controlled chamber than in the Republican-held Senate, the AP said.