British Transport Police officers want to speak to him after a row broke out on train travelling between Scunthorpe and Grimsby.
The incident happened at around 6.30pm on Saturday, 6 December.
Investigating officer PC Rachael Croft said: “A man was sitting in fold down seats near the carriage door when a man with a bike boarded the train and asked him to move so that he could put his bike in the area. The man refused.
“The cyclist then leant his bike against the carriage wall while complaining on his mobile phone about the man and a woman sitting opposite in the priority seating area.
“The man then approached the woman and took a photograph. When questioned he said it was because she was sat in a priority seat and called her pathetic.
“When the man sitting in the fold down seat intervened he was then subjected to a barrage of insults.
“The conductor was summoned and the woman stayed on board the train beyond her stop as she felt too intimidated to leave the train at the same station as the cyclist.”
Officers believe the man in the image could have information about the incident.
Anyone with information is asked to contact British Transport Police on 0800 40 50 40, or text 61016, quoting background reference PSUB/B4 of 13/11/15. Information can also be passed anonymously to the independent charity Crimestoppers on 0800 555 111.