David Davies, 61, went missing from his home in the Morningside area of the city. He was last seen at lunchtime on Monday, March 5, and has not been in contact with any of his family or friends since.
He is known to frequent the Pentland Hills area. Police are growing increasingly concerned for his welfare and are urging anyone who has seen or heard from him since he went missing to get in touch.
Mr Davies is described as being 5ft 9ins tall and of slim build, with short dark hair and hazel eyes.
He is believed to be wearing a dark duffel coat and tracksuit bottoms.
Anyone with any information should contact Lothian and Borders Police on 0131-311 3131, or Crimestoppers in confidence and complete anonymity on 0800 555 111.