The driver picked up a man and a woman in the Easterhouse area shortly before midnight on Monday night, police said.
During the journey, the couple asked to be taken to another address, where the man got out of the taxi and went into a house. He returned to the car with another man and the two of them, along with the woman, were driven to the Haghill area of the city.
But they arrived at what police described as a "disturbance" and the two men got back into the taxi and demanded that he drive off. The driver was then threatened with a gun, as the men demanded he return to the disturbance to pick the woman up. Police arrived at the scene, but the men jumped out of the taxi and ran away.
Detective Constable Dawn Bethune of Strathclyde Police said: "Thankfully the taxi driver was not injured but it was a terrifying ordeal for him.
"I would like to speak to anyone who has any information that will help us with our inquiries."