The incident happened on a train travelling between Leeds and Hull on Thursday, 25 August at around 4.45pm.
She was standing in the doorway when a man began to stroke her hand and bottom.
PC John Stubbs, of British Transport Police, said, “The victim was on her first ever train journey.
“She has been left extremely upset by what happened, and fears travelling on a train again. It is vital that we find the person responsible.”
The victim got off the train at Selby and police believe the man in the picture may have exited at Brough or Hull.
Anyone with information is asked to contact British Transport Police on 0800 40 50 40, or Crimestoppers on 0800 555 111.