John Coleman was last seen at the Access Point in Leith Street on Friday, 1 May last year.
Mr Coleman, who also goes by the names of Daniel O'Connell and Sean O'Connell, is known to live rough and travel extensively throughout the UK and Ireland.
The 51-year-old, who suffers from epilepsy, is described as being white, around 5ft 9in tall, of medium build, with brown eyes. He has medium-length brown hair and is unshaven. He speaks with a Glasgow accent, and was last seen wearing a beige jacket.
He also has two distinctive tattoos on his left arm, with "John" tattooed on his forearm, and another with a rose, dagger and Irish harp.
Inspector Andy Gilhooly said: "We know he's a bit of a loner, but he has contacts all over the UK and Ireland, and we are keen to speak to anyone who knows him."
Anyone with information is asked to contact police on 0131-311 3131 or 0800-555 111.