Robin Green, 70, was last seen on Thursday and is thought to have gone walking in Aberdeenshire.
Officers are concerned he may have spent the night outdoors and have launched a major search involving a police helicopter and mountain rescuers.
Mr Green, who lives in Aberdeen’s west end, was last seen at about 1pm on Thursday near Craigton Road in the city.
Police believe he may have gone walking in Aberdeenshire, particularly in the Glen Dye area near Banchory.
Officers appealed for walkers and residents in the area to keep a lookout for Mr Green, who is 5ft 9ins and slim, with long grey hair and a beard.
He was wearing a green wax jacket, a red jumper and dark dress trousers when last seen.
Inspector David Hoyle, who is leading the search, said: “It has been several hours now since Mr Green was reported missing to police and there are increasing concerns for his safety and welfare.
“There is a chance he may have slept outside overnight and I must ask the public to please keep an eye out for him, and to let us know if you see anyone - or have seen anyone - matching his description.
“Because of the terrain that needs to be searched we will be utilising the Police Scotland helicopter and mountain rescue support.
“I would appeal to dog walkers, walkers or simply anyone who lives in the local area to please keep a lookout for Mr Green - please check your gardens, outbuildings and the surrounding area.
“Likewise, if Mr Green could contact us directly to let us know he is safe and well I would urge him to do so.
“Anyone with information regarding the whereabouts of Mr Green, or any possible sightings of him, is asked to contact Police Scotland on 101.”