A taxi driver who allegedly indecently assaulted a female passenger in Sydney's inner west has now been charged with assaulting a second woman in a separate alleged attack a week earlier, police say.

The second woman came forward after learning that the 61-year-old driver, from Auburn in Sydney's west, had been charged this week with assaulting a female passenger in circumstances she said were very similar to her own encounter.

The alleged assaults occurred in Glebe and Newtown, after the women had hailed taxis from busy streets.

In the original alleged assault that sparked the police investigation, a 26-year-old woman told police she had hailed a taxi outside Central Railway Station to get to her Glebe home just after 11pm on Sunday.