The shootings happened around 12:15am Saturday at a mobile home park on the 4700 block of Anderson near Buxley in southwest Houston.
Houston police say Francisco Arzate kicked his way into a mobile home where 63-year-old Guillermo Pineda Valdez and his wife, Maria, were watching at least three of their grandchildren.
Arzate allegedly opened fire and shot the grandfather several times. He died at the scene, officials said.
He then shot the grandmother several times and fled. She was taken to Ben Taub General Hospital in critical condition and is expected to live.
Police said the children were not hurt.
According to officials, Arzate is the ex-common law husband of the Valdez's daughter. They had a 10-year relationship and five children together, officials said.
Investigators said Arzate contacted the Valdez's daughter yesterday and told her he was suffering since their breakup and that she would suffer, too.She was not at the home at the time of the shooting.
Police are still looking for Arzate. He is charged with capital murder.
Anyone with information on his whereabouts is urged to call Crime Stoppers at 713-222-TIPS. All tipsters remain anonymous and could be eligible for a cash reward.