Martin McGuiness (58) is a patient at Leverndale Hospital in the Pollok area, and was last seen there on Friday, September 25 at 11.30am.
He is described as a white male, 5ft 6 inches in height and of medium build with black hair and a beard. When he was last seen he was wearing a black jacket with dark-coloured trousers and boots.
Inspector Andrew Small of Pollok Police Office said: “Martin is known to frequent Glasgow city centre and I would ask anyone who has any information on his whereabouts, or recognises his description to come forward to police. I’d also appeal directly to Martin to get in touch to let us know he is safe.
“Martin has been missing before, however not for this length of time and we are becoming increasingly concerned for his wellbeing.”
Anyone with information on Martin’s whereabouts should contact Police Scotland on 101.