Steven Frame, 51, from Tiree in East Kilbride, was last seen at 2.30pm yesterday and was reported missing just after midnight last night.
He is believed to have left home in his silver car, a Nissan Pixo with registration starting SG12, but did not take money, clothes or his mobile phone.
Described as 5ft 2in, bald with blue eyes, a fair complexion and medium build, Steven was last seen wearing a black North face jacket, blue t-shirt, blue jeans and blue/grey trainers.
Sergeant Derek Callan said: "Steven's family have been looking for him since he was last seen and are now very concerned for his safety and wellbeing.
"All known areas where he normally frequents have been checked and there have been no sightings of him or his vehicle.
"I would urge anyone who knows him and has seen him since the afternoon of Thursday, April 16 or recognises the description or car, to contact police."
Anyone with information can contact Police Scotland on 101.