The victim, from Northamptonshire, boarded the 5.05pm Edinburgh to Newcastle service on Sunday May 20.
A man sat next to her and as the train departed he inappropriately touched her.
British Transport Police say he also exposed himself and tried to get the victim to touch him and accompany him to the toilets.
Officers have reviewed CCTV footage and identified a man they want to speak to regarding the incident.
Detective Constable Colin Dore said: “The man left the train at Newcastle after asking the victim to follow him to his house.
“After reviewing CCTV on the train we have identified a person we’d like to speak to about what happened and I’d urge anyone who knows who he is to contact us.
“The victim has been left extremely distressed following this incident.”
Anyone with information is asked to contact BTP on 0800 40 50 40.