In 2002, Kent Sprouse murdered a man who was pumping gas at a convenience store in Ferris, about 20 miles south of Dallas.
Then he killed Ferris officer Marty Steinfeldt, who responded to that shooting call.
Sprouse was charged with both murders, but only tried for the police officer's.
Sprouse claimed insanity at trial, but jurors rejected that defense.
The 42-year-old was the fifth Texas inmate executed this year.