The assault happened between 4.35pm and about 4.50pm on Tuesday, March 26 on the train from Sheffield to Leeds Station.
A man boarded the train at Darton rail station - the stop before Wakefield Kirkgate - and sat next to the woman.
He began trying to make conversation.
The man went on to touch the woman's knee, put his arm around her and squeeze her shoulder.
When she tried to leave, he pulled her back and attempted to kiss her.
The woman managed to get away from the man and walked down the carriage to sit with two other women.
One of the women took a photo of the suspect and police are keen to speak to this woman.
The man is described as dark-haired, olive-skinned and aged in his mid-30s.
He is described as slim, tall and wore a black and white chequered hat, a brown and beige scarf and brown clothing.
He spoke in broken English.
British Transport Police officers want to speak to anyone who witnessed the offence.
They particularly want to speak to the woman who took the photo of the suspect.
Witnesses can contact BTP by texting 61016 or by calling 0800 40 50 40 quoting reference 556 of 29/03/19.