The 18-year-old suffered upper body injuries when he was seriously assaulted on Friday night.
The attack happened between 11pm and 11.30pm in Peat Road.
The victim was walking along the road, close to St Robert's Church, when three men approached him.
One of the men then assaulted him, leaving him with injuries to the top half of his body, police said.
The injured man was taken by ambulance to the city's Southern General Hospital, where staff described his condition as stable.
The suspect is described as being white, in his 30s with short cropped hair. He was wearing a black Nike tracksuit and has a scar on his left cheek.
The two others involved were both in their 20s and had dark hair. One was wearing a light blue tracksuit and the other had a black tracksuit on.
Detective Constable Sheila MacDonald, of Police Scotland, said: "Inquiries are ongoing to establish the exact circumstances surrounding this incident and officers are carrying out inquiries in the local area and checking CCTV footage in an effort to gather more information on this crime.
"Anyone who was in the Peat Road area near to where this crime happened, and who witnessed anything suspicious, please come forward."
Police can be contacted by calling 101.