The incident happened at around 12.30am on Wednesday, September 25 in Outwood.
The 32-year-old victim, who police describe as a vulnerable man, was walking on Victoria Street when he was approached by a man who made demands for cash.
The suspect punched the victim in the face, causing him to fall to the floor. The victim's wallet was taken.
The victim suffered extensive bruising and cuts around his eye and is now afraid to leave the house after dark.
West Yorkshire Police are now searching for the suspect, who is described as under 32-years-old and taller than 5 foot 8. The victim thinks the man was wearing a black jacket at the time of the attack.
Detectives have released CCTV images of who they believe to be the suspect at the time of the offence.
Anyone with information about the person responsible for the robbery, or who was in the area and saw anything suspicious, is asked to contact the police.
Alternatively, contact independent charity Crimestoppers anonymously on 0800 555 111.