The House Travel Committee voted 9-1 in favor of a resolution that claimed wolves kill about 330 elk each year, costing the state money in lost hunting revenue.
Wolves were reintroduced to Yellowstone National Park in 1995.
Republican Rep. Louie Tomassi of Big Piney said the state should get rid of the wolves.
"We didn't bring them here," he said. "We ought to shoot them here. Who's going to take us to court?"
The state's chief game warden, Jay Lawson, said federal authority overrides state authority to manage wolves because the animals are protected under the Endangered Species Act.
The wolf population in Idaho, Wyoming and Montana has exploded in the past six years, and the predators could be removed from federal protection if all three states adopt state wolf management plans acceptable to federal wildlife managers.