The footage, which was filmed by another passenger on board, shows the driver appearing to throw the man out of the door as he shouted "Get off."
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He is then seen kicking the man before he falls to the floor, Liverpool Echo reports.
Stagecoach confirmed it had launched an investigation after the footage emerged.
In the video, believed to have been recorded in Breck Road in Anfield, a man can be heard shouting "get off" as an apparent fracas breaks out close to the driver's cab, and bangs are heard.
The driver climbed back onto the bus after throwing the man off
He appeared to kick the passenger
It then shows the driver opening the cab door and appearing to push the passenger off the bus and onto the pavement.
The driver then kicks the man, who falls on to the floor, after which the bus driver gets back on to the bus amid laughter and shocked reactions from passengers on board.
The man was bent double after appearing to be kicked
The man is seen on the footage getting up from the pavement and standing bent over double as the bus pulls away.
A spokeswoman for Stagecoach told the Liverpool Echo: "We were concerned to see this footage.
"This is not the way we would expect our drivers to deal with any situation. We will be looking into the full circumstances, and discussing the incident with the driver involved, as a matter of urgency."