Police are investigating the incident as a hate crime after the woman was subjected to verbal abuse on the London to Glasgow service, which arrived at Preston at 8.43pm on Sunday, March 13.
British Transport Police said officers at the station spoke to a man in connection with the alleged offence and ‘enquiries are ongoing’.
The force is keen to speak to anyone travelling on the service who witnessed the incident .
A police spokesman said: “The incident occurred on the 5.29pm London Euston to Glasgow service that arrived at Preston station at 8.43pm.
"At just after 8.30pm on Sunday 13 March, a woman was racially abused on-board the train.
“Officers are keen to speak to anyone that was on-board who may have witnessed the incident.”
Witnesses can contact BTP by texting 61016 or calling 0800 40 50 40 quoting reference 2200024397.