In the first robbery, two men, one armed with a knife, entered the shop at about 20:55 BST on Friday and demanded cash and cigarettes.
The second raid happened at about 07:30 BST on Saturday and again two men, one armed with a knife, stole cash and cigarettes.
Police said they "strongly believe" the robberies are linked.
Ulster Unionist councillor Jim Rodgers has said he is concerned by the number of robberies in the area.
"The police and the public need to do more to try and prevent these happening," he said.
"For those who are suffering, it is desperately serious.
"Many of us are working extremely hard to keep businesses in the east of the city and to attract new employers and this isn't helping matters."
The MP for East Belfast, the DUP's Gavin Robinson, said he was appalled by recent robberies in the area.
"Business and our wider community need reassurance that such lawlessness will not be tolerated," he said.
"The dark cloud of crime won't pass without intervention."
The men in the Albertbridge Road robberies 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 5ft 11ins 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.
A shop on the Albertbridge Road in east Belfast has been robbed twice in less than 12 hours.