Detectives investigating the robbery at the Spar in East Gate North have released a CCTV image of the offender.
He entered the shop at around 10.30pm on Friday, September 8 and demanded that the till be opened.
The shopkeeper fought him off, suffering minor injuries to his hand in the process.
The robber then ran out of the store towards Scarborough Road.
Detective Sergeant Tom Napier, from Humberside Police's Bridlington investigation team, said: "We are very keen to identify the man in this CCTV image as soon as possible due to the violent nature of this incident.
"We want to hear from anyone who may know who he is. If anyone recognises him from these CCTV pictures please contact us immediately."
The man wore a dark blue hooded jacket, blue jeans and gloves, and carried an axe with a yellow handle.
Anyone with information or who recognises the man pictured is asked to call 101, quoting log number 510 of 08/09/2017.
Information can also be passed on to Crimestoppers anonymously on 0800 555 111.