A Melbourne cab driver has been caught on camera reading a newspaper while driving in the CBD.

A passenger, Queensland councillor Paul Tully, filmed the driver's behaviour , saying it was dangerous and unacceptable.

Cr Tully caught the taxi from the airport to his inner-city hotel on Tuesday afternoon.

He said he noticed the driver swerving and driving erratically early on in the trip but was even more surprised when the driver took his hands off the wheel to read a newspaper.