The suspect waited outside Rock ‘n’ Novelties on Foreshore Road until the shop assistant’s back was turned.
He then entered the shop, approached the counter and picked up a handbag from behind the counter.
He left the building, walked around the corner and ran up Eastborough.
A shop assistant followed the man, who discarded the bag as he made off.
The incident happened on Saturday, March 25 and police have now released the image to help them with their enquiries.
The suspect is believed to be aged in his mid-60s with shoulder-length hair and a stocky build.
Anyone who recognises the man pictured is asked to contact North Yorkshire Police on 101, select option 2 and ask for PC Adam Varney, quoting reference number 12170050618.