The man is reported to have boarded a District line train at Stamford Brook and sat down opposite his victim.
Moments later he walked over to the 45-year-old man, who was standing by the carriage doors, and punched him in the face, British Transport Police said.
The attacker is then said to have walked calmly back to his seat before getting off the train at Turnham Green.
The alleged assault took place between 8.35pm and 8.45pm on October 19.
PC Nick Dipper said: “This was an unprovoked assault witnessed by other passengers, who went to the victim’s aid while the offender calmly returned to his seat.
“The offender left the Tube train at Turnham Green station.
“I am keen to speak to the man in the CCTV images as I believe he has vital information that would help with the investigation. Everyone has the right to travel on the railway network without fear or intimidation.”
Anyone who was on the Tube carriage when the incident occurred is asked to contact police on 0800 40 50 40 or text 61016 citing reference 186 of 05/12/16.
