Parr, 35, was executed by lethal injection at the state prison in Huntsville, KWTX-TV, Waco, reported. He was the fifth person executed in Texas this year.
Parr had filed his own appeal with the U.S. Supreme Court, which Justice Antonin Scalia rejected without taking it to the full court, the TV station said.
In his final appeal, Parr contended he had deficient legal help at his trial in Waco and in earlier stages of his appeal, KWTX-TV said.
Parr was convicted in the Jan. 11, 2003, slaying of Joel Dominguez, 18, and wounding of Mario Chavez, then 18, in Waco.
Authorities said Parr had bought marijuana from Dominguez at the store earlier and had returned with a friend, Earl Whiteside, to get his money back.
Dominguez returned the money but Parr shot him anyway. Whiteside shot Chavez in the hand, prosecutors said.
Whiteside pleaded guilty in 2004.
Parr maintained he didn't shoot Dominguez but wouldn't name the shooter.