A man has died in hospital two days after he was knocked to the ground in a one-punch attack in South Brisbane.

Timothy Lang, 48, was punched in the back of the head by a man outside The Fox Hotel on Melbourne Street just after 10:00am on Saturday.

Queensland Police Service said the pair crossed paths and exchanged words, before Mr Lang was struck and fell to the ground, hitting his head.

The attacker then turned and walked off in the direction of Merivale Street.

Mr Lang had been on life support in the Princess Alexandra Hospital in a critical condition, but died this afternoon.

Police are still searching for the attacker.

He is described as about 170 centimetres tall with short dark hair and was wearing black shorts with a red shirt tucked into them, and white running shoes.