Fire crews were called to Furzefield Road at around 3.45am on Friday (December 17).
West Sussex Fire and Rescue Service made Sussex Police aware of the incident.
Police said the fire is believed to have been started deliberately.
An appeal for information has now been launched.
A police spokesperson said: "No one was injured in the incident although the car had its rear window smashed and was set alight.
"There was also damage to the front door and ground floor windows of the nearby home.
"Anyone with information is asked to call 101 or report it online, quoting serial 172 of 17/12."