The incident happened around 12.15am on Thursday 2nd August in Ochiltree Crescent.
A Ford Focus parked outside an address in the street was set alight, but was quickly extinguished, causing minimal damage to the vehicle.
Inquiries are underway to trace those responsible and anyone with information is asked to come forward.
Detective Constable Barry Carlin from Livingston CID said: “Thankfully this fire did not get a chance to fully take hold or else the car could have been completely destroyed and neighbouring properties could have been put at risk.
“Anyone who remembers seeing any suspicious activity around Ochiltree Crescent during the early hours of Thursday morning, or who can help us identify the culprits, should contact police immediately.”
Those with information can contact Livingston CID via 101 and quote incident number 0048 of the 2nd August 2018. Alternatively, an anonymous report can be made to the charity Crimestoppers on 0800 555 111.