The theft took place at the Co-op convenience store at the Esso petrol station in Harrogate Road on Friday, September 15.
A North Yorkshire Police spokesman said: "The man was seen to enter the store at approximately 10.30pm. He selected a case of cider and left the store without making an attempt to pay for the items."
Anyone who recognises the man pictured or who has any information is asked to email [email protected] or call Gary Anderson on 101, quoting reference 12170166250.
Information can also be passed on to Crimestoppers anonymously on 0800 555 111.