The Grammy-award winning Canadian-born musician filed the lawsuit through his lawyers in Manhattan federal court, seeking up to 150,000 US dollars (£113,000) in statutory damages for each infringement.
A message seeking comment was left with a campaign spokesperson.
The legendary singer cited repeated use of two songs: Rockin’ In The Free World and Devil’s Sidewalk.
The campaign has used the tunes numerous times at rallies and political events, including on June 20 in Tulsa, Oklahoma, the lawsuit said.
Young said he was not suing to “disrespect the rights and opinions of American citizens, who are free to support the candidate of their choosing”, the lawsuit said.
“However,” it added, “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”.
Young first complained about the use of the 1990 single, Rockin’ In The Free World, in June 2015, when the song accompanied the Trump announcement of his presidential campaign, according to the lawsuit.
The campaign’s insistence in a statement then that it had obtained permission to use the music only proved that it was aware it needed permission, the lawsuit said.
It said Young has voiced continuous and public objections to the use of the music.
“The campaign has wilfully ignored Plaintiff’s telling it not to play the Songs and wilfully proceeded to play the Songs despite its lack of a licence,” according to the lawsuit.
New York attorney Ivan Saperstein, who filed the lawsuit on Young’s behalf along with attorney Robert S Besser of Santa Monica, California, declined to comment.
On July 3, Young lodged a complaint on the Neil Young Archives website, where a copy of Tuesday’s lawsuit was also posted, after President Trump visited Mount Rushmore for an event.
“I stand in solidarity with the Lakota Sioux & this is NOT ok with me,” he said in support of over 100 protesters who forced the closing of a road leading to the landmark.
He complained after Like A Hurricane and other songs were played when President Trump visited the site.
“Imagine what it feels like to hear ‘Rockin’ in the Free World’ after this President speaks, like it is his theme song,” Young said on the website. “I did not write it for that.”
Other artists have also complained after their songs were played at President Trump’s events.
In June, the Rolling Stones threatened to sue after the 1969 classic You Can’t Always Get What You Want was played at President Trump’s Oklahoma rally, where critics said the indoor event threatened to spread the coronavirus.
The family of the late rock musician Tom Petty said it had issued a cease-and-desist order after Trump used the song I Won’t Back Down in Tulsa.
“Trump was in no way authorised to use this song to further a campaign that leaves too many Americans and common sense behind,″ the statement said.