The hip-hop star is up for album of the year for To Pimp A Butterfly.
Kendrick Lamar’s competition comes from Taylor Swift, whose pop smash 1989 is finally nominated, a year after its release.
It came out too late to be eligible for last year’s awards, a fate which has befallen Adele’s 25 this time around.
Taylor Swift ties with R&B star The Weeknd for second place, with seven nominations apiece.
Ed Sheeran is up for two of the major prizes – song of the year and record of the year – for his emotive ballad Thinking Out Loud.
The former award goes to the writers (in this case Ed Sheeran and Amy Wadge), while the record of the year category takes into account the performance and production of a hit song.
Other nominees for song of the year include The Weeknd’s breakthrough hit Can’t Feel My Face and Mark Ronson’s global smash Uptown Funk.
Taylor Swift is nominated for the tongue-in-cheek single Blank Space, as is Kendrick Lamar for Alright, the hope-filled centerpiece of his album.
Kendrick Lamar’s domination of the shortlist is “a testimony to his artistry,” said Neil Portnow, head of the Recording Academy.
“He’s someone that’s very serious about his art and about his craft, and has been working it for quite some time. And this is one of those instances where the work pays off.”
Kendrick Lamar’s other nominations include best rap album and best pop duo/group performance for Bad Blood – a remix of one of the tracks on Taylor Swift’s 1989.
The singer is also shortlisted twice for best rap song, including Kanye West’s All Day, which he co-wrote – along with 18 other credited performers, which could make an interesting moment on stage if West wins.
Among the most prestigious awards in music, the Grammys feature an exhaustive 83 categories in 30 genres, including the likes of best tropical Latin album and best jazz improvisation.
Outside the main categories, the late Amy Winehouse is up for her seventh Grammy thanks to Asif Kapadia’s revealing documentary on her life; while a deluxe reissue of The Rolling Stones’ Sticky Fingers is up for best box set.
Justin Bieber, who had been considered a contender for some of the main prizes, only gets one nomination, for best dance recording; while Rihanna also misses out, despite her Paul McCartney duet FourFiveSeconds being tipped as a nominee for song of the year.
The Grammy Awards ceremony will take place on February 15, 2016, at the Staples Center in Los Angeles.
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