The shooting happened around 2am Saturday in a shed behind a vacant house in the 700 block of Sixth Avenue North.
Robert Mitchell Lyles, 42, died inside the shed from multiple gunshot wounds. Police said they are still trying to determine how many times he was shot.
Terrie Lynn Moffett, 30, was also shot several times. She was rushed to an area hospital in unknown condition.
Both victims are from Bacliff, and investigators are not sure what they were doing in Texas City. Lyle's SUV was found parked in front of the vacant house. Investigators said they have some leads, but they are waiting to talk to Moffett for more details.
No suspect description has been released. Anyone with information on this case is urged to call police at 409-643-5750 or Crime Stoppers at 409-945-8477.