US rapper Eminem and Lady Gaga follow closely behind.
The 23-year-old S&M singer is up for hot 100 artist, top female artist, and R&B artist, as well as her collaboration with Eminem, Love the Way You Lie, being up for six awards.
Eminem, 38, has 16 nominations, including rap artist and top male artist, while Gaga, real name Stefani Germanotta, has 12.
They are up against Rihanna, Justin Bieber and Taylor Swift for top artist.
Bieber, 17, has managed to get 11 nominations and could win the top new artist prize.
There are 46 categories at this year's awards and the winners are decided by Billboard chart rankings.
The winners will be announced at an awards ceremony in Las Vegas on May 22.