The child was attacked on the 4pm Edinburgh Waverley to Peterborough Virgin East Coast service on Sunday, February 12.
British Transport Police said the man was white, around 5ft 10ins, in his late 30s and of a large build.
He had short black spiked hair and was wearing glasses, a black and white polo shirt, dark coloured jacket, a thick metal chain around his neck, dark grey jeans and white trainers.
He had a tattoo on his right arm and has a north-east English accent.
Investigating officer PC Joss Froggatt asked for anyone who recognised the man to contact British Transport Police on 0800 40 50 40 or by texting 61016 – quoting reference ‘324 of 12/02/2017’.