The victim, a 37-year-old man, was approached by three youths as he walked near the children's play area in Cross Flatts Park in Beeston.
They demanded money from the man and followed him when he refused.
The youths then punched the man to his head and body, before hitting over the head with a bottle.
Police said the trio took a carrier bag of shopping from him and emptied it on floor, but nothing was taken during the incident at around 7.35pm on January 3.
PC Thomas Enevoldsen, of Leeds District Crime Team, said: "This was clearly a very frightening ordeal for the victim and we are carrying out extensive enquiries to trace the people responsible. We would like to hear from anyone who witnessed the incident or who may have seen these youths in the area at the time."
The man suffered a cut to the top of his head when the bottle smashed. He was taken to hospital and discharged later that night.
Forensic work is ongoing after the scene was examined on the night and the incident is being investigated as a robbery.
The youths were described as white and aged 15 to 16.
Anyone with any information is asked to contact PC 1537 Enevoldsen at Elland Road via 101, quoting crime number 13170003680.
Alternatively, call the independent charity Crimestoppers anonymously on 0800 555 111.