CCTV images of the car involved in the collision have been released by South Yorkshire Police in a bid to find the driver.
A car struck an 80-year-old man as he crossed Southey Green Road, near to the junction with Halifax Road, Southey Green, at 5.40pm on Friday, September 13.
The vehicle, which failed to stop at the scene of the collision, is understood to have turned from Halifax Road onto Southey Green Road just before the incident.
The pedestrian was taken to hospital with serious injuries but has since been released and is recovering well.
Witnesses or anyone with information or suspicions should call South Yorkshire Police on 101 and quote incident number 705 of September 13.