The robbery, in West Way, Heston, on Sunday June 7, left the 51-year-old man with serious facial injuries.
He was walking along the back street at around 11.40pm, according to police, when he was hit from behind with a blunt object, causing him to fall to the floor.
The assailant, described as a white man wearing a baseball cap and hooded top, continued to attack the man on the ground and took an unspecified amount of cash before fleeing west along West Way.
Trainee Detective Constable Craig Boosey, of Hounslow Serious Acquisitive Crime Unit, said: "This was a horrific attack on a man that left him with serious facial injuries to the point that doctors were worried that he may lose his sight in one eye.
"I am urging anyone who may have seen anything or knows who carried out this robbery to contact the police.”
No one has been arrested in connection with the robbery, and police enquiries are ongoing.
Anyone with information is asked to call TDC Boosey on 020 8247 6650, or Crimestoppers, anonymously, on 0800 555 111, quoting reference 0511485/15.