Police are appealing for witnesses after the attemptin the Willowbrae area last night.
The incident happened around 8.45pm within Nairne Convenience Store on Lady Nairne Place.
A woman threatened two male members of staff with a knife, while a man tried to open the till.
The attempts failed and the suspects ran from the store towards Lady Nairn Grove.
The woman was described as being mid-twenties, 5ft tall, with a heavy build and wearing dark clothing. She was concealing her face.
The male is described as also being in his mid-twenties, similar height, with a medium build and wearing dark clothing. He was also concealing his face.
Officers are now urging anyone who can assist with their enquiries to come forward.
Detective Constable Jonny Wright of Craigmillar CID said: “This was a seriously distressing incident for the people involved and I would urge anyone who saw the suspects or any suspicious behaviour in the area at the time of the robbery to contact us immediately.”
Anyone with information is asked to contact Police Scotland on 101 or contact Crimestoppers anonymously on 0800 555 111.