At 5.45am on 5 March, officers were called to reports that a man armed with a handgun had entered One Stop on Station Road.
He threatened a member of staff and stole a quantity of cash before leaving the shop.
No one was physically injured during the incident.
The offender is described as being approximately six feet tall with large eyebrows. He was wearing black clothing and had a black scarf covering his face.
A cordon was put up to allow crime scene investigators to examine the scene.
Detective Inspector Andrea Power, of Weymouth CID, said: “I am appealing to anyone who was in the Station Road area at the relevant time and saw a man acting suspiciously to please get in touch.
“I would also urge anyone who recognises the man in the image from the clothing he was wearing to come forward.”
Local officers have been carrying out reassurance patrols in the area and can be approached with any concerns.
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