Officers said they received a 911 call from the male victim around 7 p.m. Friday and responded to the home on Deer Ridge Drive.
The man was found in the front yard of the home with multiple stab wounds, and the woman was observed through a window inside the living the living room, investigators said.
Police said the suspect, Juan Jose Uribe Pelaez, 32, was also inside the home.
First responders said they used a drone to track his movements before officers deployed a Taser and took him into custody.
The woman was pronounced deceased, and the man remains hospitalized, police said.
Uribe Pelaez is charged with murder and aggravated assault with a deadly weapon, according to officers.
League City police confirmed to ABC13 that the suspect is the victims' son.
Police haven't released a motive.