At around 9pm on Saturday 28 March the 16-year-old victim boarded a train at Manchester Oxford Road towards Horwich Parkway.
A man, who appeared to be travelling with a group of friends, was already seated in front of the victim on a table seat. He approached the 16-year-old victim and straddled her.
A fellow passenger tried to intervene, telling the man to leave the victim alone. He then became abusive, swearing and insulting her.
Investigating officer PC Kirsty Hansell said: “The young girl was extremely distressed by the man’s actions and was left feeling scared. The man had previously approached at least two other passengers in the same manner.
“This incident has left both victims fearful of travelling unaccompanied on the railway. Behaviour like this which frightens and intimidates other passengers will not be tolerated.
“We need to speak to anyone who saw what happened. Please get in touch.”
Anyone with information is asked to contact British Transport Police on 0800 40 50 40, or text 61016, quoting reference PSUB/B7 of 01/05/2015. Information can also be passed anonymously to the independent charity Crimestoppers on 0800 555 111.