According to Pearland police, 38-year-old Geoffrey Ferguson told a friend he was responsible for the killing.
The shooting happened on Sunday just before 5 a.m. in the 1600 block of Rayburn Lane.
Officers responded to the home and saw Ferguson inside a bedroom and took him into custody, police said.
They found the body of his 69-year-old father, William Ferguson, in another bedroom with multiple gunshot wounds.
It's still unclear what led to the shooting, but there were no other suspects or victims involved in the incident, police said.
Geoffrey Ferguson called a friend and told them about the killing, according to investigators, and that person was the one who called 911.
The incident remains under investigation.