The incident happened on board a service travelling between Edinburgh and Montrose are appealing for further information.
On Friday, October 22 a man boarded the 8.32pm service from Edinburgh Waverley, and a woman on board noticed he was staring and waving at her.
He then sat next to the woman and began to make sexual remarks towards her, before sexually assaulting her.
The man is described as a black male or medium build, around 6ft tall, and with a scar above his eyebrow.
At the time he was wearing a navy Moncler jacket, black jeans and blue and white trainers.
Officers from the British Transport Police are keen to speak to anyone who was on the train and may have witnessed the incident and who could assist with their enquiries.
Witnesses, or anyone with relevant information, can contact BTP by texting 61016 or calling 0800 40 50 40 and quoting reference 705 of October 22, 2021.
Alternatively, you can call Crimestoppers completely anonymously on 0800 555 111.