The culprit, who was also wearing a Deliveroo company jacket, confronted two staff members during a raid at the One Stop on Hyde Park Road shortly after 9.10pm on Tuesday.
He had a bulge in his pocket and demanded cash from the till, which he put into a bag along with alcohol and cigarettes.
Detective Inspector Richard Holmes, of Leeds District CID, said: “Although no gun was seen during the robbery, it was clearly a very frightening experience for the victims.
“We are carrying out extensive enquiries into the incident and would like to hear from anyone who witnessed the incident or saw the suspect in the vicinity.”
After the offence, the robber fled down Hyde Park Road towards Hyde Park Terrace.
He was wearing a light blue Deliveroo jacket and shiny silvery white tracksuit bottoms and was carrying a black bag
Anyone with information is asked to contact Leeds District CID via 101 quoting crime number 13180156667 or call the independent charity Crimestoppers anonymously on 0800 555 111.