Jesse Braham has claimed in legal papers Taylor Swift stole the words from a song he wrote in 2013 called Haters Gone Hate.
As well as the monetary compensation, the R&B singer also wants his name added as a writer on the track.
Representatives for Taylor Swift have yet to officially comment on the legal case.
Shake It Off topped music charts around the world and reached No 2 in the UK. The video for the song has been watched more than 1.1 billion times on YouTube.
Jesse Braham – who goes by the stage name Jesse Graham – claims he has copyright ownership of the phrases “haters gone hate” and “playas gone play”, which appear in the chorus of Taylor Swift’s song.
In his song, the chorus comprises: “Haters gone hater, playas gone play/ Watch out for them fakers, they’ll fake you everyday.”
The chorus of Shake It Off features lyrics including: “Cause the players gonna play, play, play, play, play/ And the haters gonna hate, hate, hate, hate, hate.”
Taylor Swift sings another line: “And the fakers gonna fake, fake, fake, fake, fake.”
Apart from the lyrical similarity, the songs bear no resemblance musically.
Jesse Braham, 50, told the New York Daily News he believed there was “no way” Taylor Swift could have penned the lyrics independently of his song.
“Her hook is the same hook as mine. If I didn’t write the song Haters Gone Hate, there wouldn’t be a song called Shake It Off,” he said.
The singer added he had spoken to Taylor Swift’s record label, Big Machine, four or five times about the issue.
He originally asked to be named as a writer and requested a selfie with the pop star, but was repeatedly dismissed and told his claim had no merit.
“At first I was going to let it go, but this song is my song all the way,” Jesse Braham said.
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