Two children - 6 and 8 years old - called 911 after they say their parents were the ones shot in the 600 block of 25th Street near Broadway Street.
Officials do not think the children witnessed the shooting.
The Galveston County Sheriff's Office confirmed the death of the woman and the man was flown to a trauma center.
GCSO deputies believe this was domestic violence incident and are still looking into how the situation unfolded.
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