It happened around 11:15am in the 5200 block of North Shepherd Drive near Pinemont Drive.
Police say the victim is a man in his 40s who lives in the neighborhood. According to officials, a black man in a white Pontiac or Buick sedan was pulling out of a Valero gas station when the car ran over the victim and kept going. Several witnesses tried to chase the driver, but he got away.
The victim was taken to Ben Taub General Hospital in critical condition with severe head injuries.
Investigators are reviewing surveillance video to try to identify the vehicle and the driver. Anyone with information on this crime is urged to call police or Crime Stoppers.