It happened around 5:35 p.m. Thursday at a home in the 6500 block of Hogue Street, just northwest of Hobby Airport.
The Houston Police Department says when firefighters arrived, they found a 72-year-old man on the couch with multiple gunshot wounds.
Homicide investigators are continuing to investigate.
A fire captain on scene told ABC13 they believe the fire was intentionally set.
Witnesses reported seeing smoke coming from the house and immediately called 911, police said.
HPD homicide detectives and HFD arson investigators are conducting the investigation.
Anyone with information in this case is urged to contact the HPD Homicide Division at 713-308-3600 or Crime Stoppers at 713-222-TIPS.