The raider targeted the shop in Great Western Road, Anniesland, on Monday and threatened a female member of staff with a knife.
He demanded cash, but the 19-year-old worker was unable to open the till, and he fled empty handed.
The man ran off towards Ancaster Drive. He is white and between 20 and 25.
Police said he had short cropped blond hair, with a scar on his left cheek.
He was wearing a light blue hooded jacket, dark jeans and white trainers.