The incident took place on South Bridge, near the junction with Niddry Street, at around 5.15am on January 1, 2019.
A 29-year-old man was struck to the face, sustaining a serious injury, and attended hospital as a result.
Police say the man pictured may be able to assist with their investigation and anyone who recognises him is asked to come forward.
The man is described as mixed-race, with short black hair, aged 18 to 21, slim and around 5ft 7in.
He is pictured wearing a black hooded jacket, black trousers, a red-coloured item near his waistband and dark-coloured trousers with a white rim.
Detective Constable Darren McDonald of Edinburgh’s CID said: “The victim sustained a painful injury following an unprovoked attack, and we believe the man pictured have information which could be of assistance to our investigation.
“We’re now appealing for the public’s help as part of our enquiries and would urge anyone who recognises him, or who may have been in the area at this time and has information of any relevance, to come forward.”
Those with information can contact Police Scotland via 101, quoting incident number 2148 of January 1, 2019, or report this anonymously to the charity Crimestoppers on 0800 555 111.
Sign up to our newsletter: enter your email in the box at the top of this article to get daily updates straight to your inbox.