Boroondara Crime Investigation Unit detectives are investigating the fraudulent use of a credit card in Hawthorn and Elsternwick in July, Victoria Police say.
Investigators believe that a man entered a Glenferrie Road supermarket on 27 July and used a stolen credit card to purchase items.
The man was wearing a dark black beanie, brown jacket and dark blue jeans. The man had a distinctive medical dressing on his left cheek and his right thumb was bandaged.
Investigators have released images of the man who they believe may be able to assist with their enquiries.
Anyone with information is urged to contact Crime Stoppers.