The execution of Jamie McCoskey, 49, was carried out at the state prison in Huntsville, a corrections employee told UPI by phone.
KWTX-TV, Waco, reported McCoskey's attorneys did not file any last-ditch appeals to try head off his execution. The U.S. Supreme Court declined to review his case previously this year.
McCoskey was found guilty of kidnapping a Houston couple, then raping the pregnant woman and stabbing her boyfriend to death, KWTX-TV said.
Texas has one more execution scheduled this year, the TV station said.