The incident happened on a Transpennine service between Leeds and Manchester on June 10.
At about 12.30am, a man boarded a delayed train at Leeds station and started to verbally abuse passengers around him, including an Asian family who he subjected to racist comments.
His manner was described as aggressive and threatening and at Huddersfield station he was forced to leave the train due to his behaviour.
Officers from British Transport Police would like to speak to the man in this CCTV image because they believe he may have information which could help the investigation.
PC Andrew Jones said: "No one should be subjected to racial or any form of abuse while travelling on the rail network – and we take every complaint seriously.
“This man’s behaviour was unacceptable, and I urge any that has information about this incident to call us on 0800 40 50 40 or text 61016, quoting 202 of 20 July. Alternatively you can ring Crimestoppers anonymously on 0800 555 111.”