The incident happened at 7.12pm last Tuesday (May 1) when a man got on the ScotRail service, from Glasgow Queen Street, at Croy station.
During the journey the man targeted a woman with racial abuse before making homophobic comments at other passengers.
The woman was very alarmed by this man’s behaviour and abuse.
The suspect is described as white, around 5’9” of medium build and was clean shaven. He was wearing a navy blue hat, a white polo shirt and black shorts.
He had on grey Adidas trainers and had a tattoo on his left arm.
Officers are keen to speak with anyone who was on board the service and witnessed what happened. Likewise, if you know someone matching the description of the suspect, please get in contact.
Information can be passed to BTP by sending a text to 61016 or by calling 0800 40 50 40 quoting reference 542 of 30/04/2018.
Alternatively, ring Crimestoppers anonymously on 0800 555 111.