In the first robbery, two men, one armed with a knife, entered the shop on the Albertbridge Road at about 8.55 pm on Friday and demanded cash and cigarettes.
The second raid happened around 7.30 am this morning and again two men, one armed with a knife, stole cash and cigarettes.
Police said they “strongly believe” the robberies are linked.
The men in both cases were described as being of slim to medium build and both were wearing gloves and baseball caps.
One of the men was taller than the other, at 5 ft 11 ins tall.
He was said to have been wearing track bottoms, Converse shoes and a blue jacket with a lighter hood.
The second man was about 5ft 7ins tall and was wearing dark jogging bottoms, white trainers and a navy zip-up jacket.
Police have appealed for witnesses to contact detectives at Musgrave PSNI station on the 101 non-emergency number.