Former prime minister Julia Gillard says the "unconscious bias" against women has to go as the Greens push for a Senate inquiry into the retirement gender gap.

"Women earn 4 per cent less in their first graduate job than men with the same qualifications," Ms Gillard told an ANZ Women's Initiative lunch in Sydney on Wednesday.

Julia Gillard with David Gonski at the ANZ Women's Initiative lunch in Sydney on Wednesday. Credit:Louise Kennerley

"For most women, that pay differential is the start of a cycle of financial inequality that becomes harder and harder to rectify," she said. "One of the issues we must confront is unconscious bias ... we are still driven by cultural stereotypes."

The comments come after ANZ bank launched a series of initiatives including free financial advice for female customers if they have less than $50,000 in their superannuation, and will pay women staff a $500-a year top up to their retirement savings.