Jessie Braham claims 25-year-old Swift's hit borrows heavily from a song he wrote in 2013 called "Haters Gone Hate", reported TMZ.
He has claimed ownership of the phrase "haters gone hate", and alleged Swift used it more than 70 times in her song.
His lyrics are, "Haters gone hate/players gone play. Watch out for the fakers/they'll fake you every day."
Some of the lyrics in Swift's 2014 hit are, "Cause the players gonna play, play, play, play, play/And the haters gonna hate, hate, hate, hate, hate."
The songwriter has demanded USD 42 million from Swift, and wants his name added to any new release of "Shake It Off".
A representative for Swift has yet to comment on the report.