Josh Hill, son of Damon, finished 8th and 13th for the opening two rounds of the Ginetta Junior Championship at Brands Hatch this weekend.
The Junior series for young drivers is running as a support series to the British Touring Car Championship this year.
Josh qualified his Tollbar Racing car on the third row of the grid in sixth place before going on to finish 8th in the first round, 11.054 seconds behind race winner Dino Zamparelli.
In the second race the 17-year-old dropped back to 13th place finishing a couple of tenths behind Race 1 winner Zamparelli and 12 seconds behind the Race 2 victor George Richardson.
Damon Hill has been open about his son’s desire to follow in his footsteps and insists the desire to race comes firmly from within Josh himself.
"From what I have seen of him in karting, I think he has some talent, and like any young teenager, he wants to find something exciting to do," the 1996 world champion told Motorsport News.
"This whole idea has been driven by Josh – he is very much leading me in this, and I think it’s great that there is something that he is so enthusiastic about," he added.
But the former Williams Renault driver has expressed concerns about exposing his son to the dangers of motorsport.
"We all love to protect our children from the risks in life but then we also deprive them of the enjoyment," he told The Times last year.
"I will reluctantly throw myself at the mercy of the fates or whatever is out there."