The Des Moines Register poll showed Romney, the former governor of Massachusetts, down one point to 29 percent from its poll in May, while Thompson, a former senator from Tennessee, emerged with 18 percent after entering the race in late summer.
Mike Huckabee, the governor of Arkansas, and Rudy Giuliani, the former mayor of New York, vied closely for third place with Huckabee rising slightly to 12 percent and Giuliani falling six points to 11 percent from the May poll, the Register reported Sunday.
Poll support also eroded for Sen. John McCain of Arizona, who dropped to fifth place with 7 percent.
Rep. Tom Tancredo of Colorado followed with 5 percent and Rep. Ron Paul of Texas with 4 percent while Sen. Sam Brownback of Kansas tied with activist Alan Keyes at 2 percent and Rep. Duncan Hunter of California got 1 percent.
The poll had a margin of error of plus or minus 4.9 points.