The pellet smashed through the driver's door window, narrowly missing Ronnie Martin.
His cab was hit again, this time the pellet went through the a passenger window.
Ronnie was not injured but was left badly shaken.
Police have launched an investigation into the incident which happened at around 8.45pm on Wednesday in the city's Royston Road.
It follows a string of incidents where vehicles, including buses, have been hit with missiles on the same stretch of road.
Ronnie, 54, who is convinced he was targeted with an air gun, said: "It's just fortunate there wasn't anyone in the back seat.
"It could have taken my eye out and I would have lost control of the vehicle."
The incident happened while Ronnie, a dad-of-one from Rutherglen, was driving along Royston Road, at the Royal Infimary.
He said: "I was just driving along and I heard a huge smash. I don't think I realised how serious it was. They were aiming directly at me.
"The police said there had been three or four incidents in the last couple of weeks but aimed at buses.
"I've been hit with snowballs and stones before but never this. It's pretty shocking."
Stephen Flynn, vice chairman of Glasgow Taxis, said: "News of this incident is of great concern to the Glasgow Taxis Committee, as the safety of drivers is of paramount importance.
"It is also a reminder of the dangers our drivers can encounter while working day or night throughout the city and beyond. Thankfully Ronnie wasn't injured in this mindless attack, perpetrated by what I can only describe as a reckless individual who I hope is quickly apprehended by the authorities and brought to book.
"We are also grateful that Ronnie wasn't carrying a passenger when this distressing incident occurred."
A police spokeswoman said: "We received a report from a taxi driver that his cab had been shot at by an air rifle. Inquires are ongoing."
A spokeswoman for First Glasgow said: "We can confirm that an incident took place on one of our service 19 buses at 6.35pm on October 29.
"Our bus was travelling along Royston Road towards the city centre when two windows were broken and one panel of glass from the door was broken.
"It is not known what caused the damage.
"This is a despicable act of vandalism. No passengers were injured.
"We have zero tolerance to such attacks and we are working closely with Strathclyde Police.
"With the increasing use of CCTV we have reduced such incidents in the past.
"We take incidents like this very seriously and would urge anyone to pass any information they have about the vandal to the local police."
Justice Minister Kenny MacAskill has vowed to strengthen the law on air weapons. At the moment people do not require a licence to have an airgun.