Police have arrested a woman who unleashed a racist tirade on a packed peak-hour train.

She was arrested at Wyong railway station on the central coast about 6pm on Thursday night, a police spokesman said.

The woman, whose real identity is yet to be confirmed, was then taken to Wyong police station to answer questions.

Earlier in the day, the woman, who identified herself as 55-year-old Sue Wilkins, apologised and said she'd had a "really really rotten day".

Ms Wilkins was filmed hurling abuse at passengers, including children and an Asian woman, in a rant apparently triggered when she couldn't find a seat on the train.