Firefighters from East Preston Fire Station were called to Josh Bates’ Volkswagen Polo, parked outside his house in Canterbury Road, Rustington, after neighbours raised the alarm at about 11.45pm on Saturday.
The 22-year-old’s mother Sharon said the first they knew of the fire was when firefighters knocked on their door to tell them.
She said: “There was lots of smoke and it just smelled horrendous. The bonnet came right up, the tyres had burst and bits of engine had flown out.”
Fire crews used two breathing apparatus and two hose reels to put out the flames, but the car was destroyed. They left the scene at around 12.30pm on Sunday.
Police officers went to the house later that morning.
Firefighters believed the fire could have been caused by an electrical fault, Sharon said, but Sharon believed arsonists had deliberately targeted her son’s car.
He had used the car from about 3pm to 3.15pm on the day of the blaze.
Sharon said: “Josh is absolutely gutted. He thinks someone has done it deliberately. Apparently it’s all over Facebook.”
She added: “We want to know who did it. People across the road said they heard someone running down the alley nearby.”
On Monday, Sharon said they found out Sussex Police had closed the case, having expected an officer to visit them and take a statement. She said: “I just think it is absolutely disgusting.
“They have made no effort to look into what went on.
“They haven’t even been out to see us.”
In response, Sussex Police said: “No lines of enquiry have yet been established, but anyone with any information about the incident or who may have witnessed anything suspicious in the area in the time leading up to it is asked to report online or call 101 quoting serial 21 of 10/05.”