The 26-year-old passenger was touched inappropriately by a teenaged boy.
The incident happened on Friday, March 20 at 3.10pm.
Police say the victim about to leave the 14.37 Glasgow Central to Motherwell service, at Motherwell, she was assaulted.
Detectives from British Transport Police are now appealing for witnesses to come forward.
The suspect is described as around 17 years old, of slim build, with short hair and about 5'7" in height. He was wearing a light blue tracksuit top, dark tracksuit trousers and carrying a rucksack.
Detective Constable Andrew Egan, the officer in charge of the case, said: "There is absolutely no excuse for this sort of unwelcome and unwarranted behaviour and I am therefore appealing for anyone who was on the train or at the stations and can help our ongoing enquiries to identify the male youth to get in touch."
CCTV footage will be reviewed in attempt to identify the man.
Anyone with information is asked to contact British Transport Police on 0800 40 50 40 or call Crimestoppers on 0800 555 111.