The rock star says the US president breached copyright laws by playing his songs at political rallies and events.
A New York court heard on Tuesday that the Canadian objected to President Trump's use of Rockin' in the Free World and Devil's Sidewalk.
The Trump campaign has not yet commented.
Young said he had complained about Mr Trump's use of his music since 2015, but had been "wilfully" ignored.
Young, who is now officially a US citizen after having lived in the country for decades, is seeking damages of up to $150,000 (£114,400) per infringement.
These include a Trump rally in Tulsa, Oklahoma, in June, and the US president's visit to Mount Rushmore in July.
'Ignorance and hate'
"This complaint is not intended to disrespect the rights and opinions of American citizens, who are free to support the candidate of their choosing," Young's lawyers said.
"However, Plaintiff in good conscience cannot allow his music to be used as a 'theme song' for a divisive, un-American campaign of ignorance and hate."
The 74-year-old has been inducted into the Rock and Roll Hall of Fame twice - first as a solo artist, and then with his old band Buffalo Springfield.
He's not the only musician angry with the US president for having used their material.
Last month, The Rolling Stones warned President Trump that he could face legal action if he continued using their songs at his campaign rallies.
Mick Jagger and Keith Richards also joined artists including Aerosmith and Elton John in recently signing an open letter calling on politicians to obtain permission before playing their music at campaign and political events.