Officers say George Stewart has recently been receiving hospital treatment and may appear confused.
He was last seen in the Springfield area of Fife by medical staff on Monday at around 12pm.
The 31-year old is described as white, slim build, around 5ft 7in tall, and with fair hair. He is believed to be wearing a blue t-shirt with white writing, blue denim jeans and black training shoes.
Officers are also asking residents to check sheds and outhouses in order to assist them in finding George.
Inspector Stephen Kay said: "We are growing increasingly concerned for George's welfare and we are appealing to the public for any information regarding his whereabouts. If you have any information on George's whereabouts, please contact Police Scotland on 101 or Crimestoppers on 0800 555 111."
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