The suspect joined the ScotRail service from Glasgow Queen Street at Croy station at around 7.12pm on Monday evening.
He is alleged to have targeted a woman with racial abuse before making homophobic comments at other passengers during the journey to Falkirk.
Officers from British Transport Police said the woman was left distressed by the incident.
The suspect is described as white, approximately 5ft 9ins 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 want to speak to anyone who was on board the service and witnessed what happened.
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.