The incident happened on the 20:14 service, between Keith and Elgin, on Friday 16 June at about 21:20.
The suspect - believed to be travelling with about seven other men - then got off the train at Elgin.
He was white, about 25, and 6ft tall. He was wearing a black and white top and sunglasses.
Det Con Nick Ritchie, of British Transport Police, said: "No-one has the right to treat another person like that.
"We're determined to stamp out this kind of behaviour from our rail network, so please, if you know this man, let us know."
Anyone with information can text 61016 or call 0800 40 50 40, quoting reference 682 of 16 June.
An appeal for witnesses has been made after a woman was inappropriately touched on a train travelling between Aberdeen and Inverness.