The incident happened in Edinburgh city centre at around 5pm on Friday.
Police said the 27-year-old victim was on a number three Lothian Bus travelling east along Princes Street when another man started to cause a disturbance.
A number of people told him to calm down but an “altercation” between the two men ensued after they got off the bus at the same stop, outside the Apple store.
The victim was punched in the face before members of the public intervened.
He then walked up Waterloo Place towards Regent Road and was struck on his head from behind. When he turned round, he realised that the same man was responsible.
The suspect then ran off up the steps towards Calton Hill, police said.
Anyone who can help police identify him is being urged to come forward.
The suspect is described as black, in his early twenties, 5ft 11ins tall with a slim build. He was wearing a white baseball cap with a red brim and a white top with blue diagonal stripes on the shoulders.
Detective Sergeant Neil Spowart said: “We believe this attack stemmed from the victim’s involvement in trying to stop the suspect causing a disturbance on the bus and are keen to hear from other passengers who were on board at the time.
“In addition, members of the public who witnessed the altercation outside the Apple store or the second assault on Regent Road are also asked to contact police immediately.”