The assault occurred at a car park on George Street in Sunshine early on December 15, hours after the attacker approached two men sleeping rough in the stairwell about 3am.
The attacker is believed to have sat with the men for hours, then became angry when they asked him to leave so they could sleep.
He then allegedly then locked one of the men outside and stomped on the other man's head a number of times while he lay on the ground.
The attacker then headed toward Kennedy Street while the uninjured man called 000.
It's believed he also stole the victim's phone and wallet.
The 34-year-old victim suffered serious head injuries.
Police have released CCTV and a photo of a man they are searching for.
He is perceived to be of African or Islander appearance and aged between 20 and 40-years-old.
He was wearing a black hooded jumper, light pants, black shoes and a black backpack.
Anyone who witnessed the incident or has information that could assist investigators is urged to contact police.