Teville Road has been partially shut while a crew attended.
Martin Cooper, from Horsham, was driving on the way to see a friend when he saw smoke coming out the front of his car.
“There was smoke everywhere, I could hardly see anything,” he said.
The 65-year-old, who has recently retired, said he managed to stop on the side of the road.
The front of the car had caught fire and he called the fire service, who put out the flames.
He believes the fire was caused by overheating.
Mr Cooper was the only person in the car and was not hurt.
He said he was not frightened by the incident and said: “These things happen.”
A spokesperson for West Sussex Fire and Rescue Service said they were called to Teville Road at 9.13am.
Two crew members wore breathing apparatus to put the blaze out, the spokesperson said.
They left the scene at 9.43am.
The lane remains closed.
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