Two men have been dragged along the road by Melbourne taxis in almost identical incidents one week apart.

In the most recent incident, a 29-year-old man was pulled along the road by a taxi in the CBD after the driver refused his fare and sped off while his arm was caught in the window.

The man had attempted to hail the taxi in Flinders Street between Swanston and Russell streets around 3.30am last Sunday.

When he requested to be taken to Brunswick, the driver allegedly accelerated quickly.

The man's arm became stuck and he was dragged about 50 metres along the road. The driver continued to accelerate before the man fell free, narrowly missing the wheels of the taxi.