John Suskis, 52, has not been seen since 11am on Wednesday, June 28.
Officers are concerned for his wellbeing and are urging anyone with information to contact Police Scotland.
Police have today released an image of John in The Waiting Room public house in Belhaven Terrace. The image was captured in the early afternoon of Wednesday, June 28. This is his last known sighting.
Inspector William Faulkner, of Howdenhall Police Station, said: “John has now not been seen for some time and we are growing increasingly concerned for his welfare.
“I would ask anyone who has seen John, or recognises his description, get in touch with us as soon as possible.”
John is described as white with tanned skin, 5ft 7ins, long dark hair with grey streaks.
He was last seen wearing a dark green trousers, brown leather shoes with a white trim around the heel, a black leather jacket and a dark checked baseball cap.
Chief Inspector Gillian Geany, also of Howdenhall Police Station said: “John has not been seen since Wednesday, June 28, and we are now very concerned for his welfare.
“I would ask those living in the Morningside area, or those who were in The Waiting Room on Wednesday afternoon, to come forward if they have seen John.
“Anyone who does know where John is, or recognises his description, is asked to get in touch with us as soon as possible.”
Those with information can contact officers at Howdendall Police Station on 101, quoting incident number 0511 June 29.