The raider targeted Poundland in Great Western Road, Anniesland, 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.
It happened at around 6.15pm on Monday.
The suspect, who made off on foot in the direction of Ancaster Drive, is described as white, between 20 and 25-years-old.
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.
Detective Constable Michael Fleck, from the robbery unit, has appealed for any witnesses to come forward.
He said: "This was a harrowing ordeal for the member of staff and it is fortunate she was not harmed during this incident.
"It is believed that the suspect had been loitering in the area prior to entering the shop.
"I would appeal to anyone who was either walking or driving in Great Western Road shortly after 6pm last night and saw this man to come forward.
"The area would have been busy with people returning home from work.
"I would ask them to think back to Monday evening and whether they saw anything that may be useful to this inquiry."