David Davies, 61, from Morningside, was last seen in the Kirkliston area at around 6.30pm last Monday after leaving his home at lunchtime.
He has not been in touch with friends or family since.
Anne Craigen said: “I have not heard from David in over a week, and I am very worried for him. I am appealing to anyone who has seen or heard from him since he went missing to get in touch with police.”
Mr Davies is described as 5ft 9in tall and of slim build with short dark hair and hazel eyes. He was wearing a dark duffel coat and tracksuit bottoms.
Police are also trying to find a woman who has been missing since last Wednesday.
Khalsoam Ali, 40, from Leith, is described as Asian, 5ft 4in tall, of medium build with straight dark brown hair with a fringe, dark eyes and has a large freckle on her right cheek.
Anyone who can help in either case is asked to contact police on 0131-311 3131