No one in the comically crowded field is expected to win a majority of Tuesday's vote. The top-two finishers will meet in a May 27 runoff.
Stockman is a congressional renegade and former homeless man known for inflammatory gun-rights comments and calls to impeach President Barack Obama.
Stockman originally filed for re-election in his suburban Houston district. But he changed his mind Dec. 9 and instead challenged U.S. Sen. John Cornyn in the Republican primary.
Those vying to replace him included two mayors and a former mayor, an insurance agent and a mortgage banker.
The runoff winner faces Democrat Michael Cole, a 2012 Libertarian congressional candidate who sought his new party's nomination unopposed.