Investigators say Lee Sims told a neighbor that he shot 42-year-old Angela Gray in self-defense.
Multiple friends say Sims and Gray had been dating and that she'd recently moved into his home in the 7200 block of Mallard Drive.
Police say a woman called them just before 3 p.m. to report a concerning phone call she'd had with Gray.
She told officers she could hear Gray and Sims "getting into it," followed by heavy breathing. She said Gray then stopped communicating.
Court documents say home surveillance video shows two people walking into the garage. A door can then be heard slamming shut, followed by two gunshots.
Gray was found dead in the living room with a gunshot wound to the chest, the criminal complaint notes.
Investigators say they found Sims with a gun concealed in his waistband.
He's being held in the Galveston County Jail on a $250,000 bond.
Gray was a nurse at an assisted living facility and the mother of two, her friends and family confirm.
Records show Sims was licensed as a security officer until last year. He has no criminal history in Texas.
Police said the investigation remains ongoing. Authorities said anyone with information regarding the incident is encouraged to contact Detective Charles at (409) 643-5763 or Detective Stinson at (409) 643-5200, adding that anonymous tips may also be submitted to Crime Stoppers at (409) 763-8477.