West Sussex Fire and Rescue Service was called at around 3.15pm to the vehicle, which was parked in Marine Parade, Worthing near the bowling alley.
One appliance attended from Worthing Fire Station, and firefighters using two pieces of breathing apparatus and a high pressure hose reel put out the flames.
The incident was left with police and the vehicle owner. The cause of the fire is currently unknown.
Fire crews left the scene at just before 4pm.