Ocean and the 'We Are Young' group are in contention for six awards, along with Mumford & Sons, Jay-Z, Kanye West and Black Keys member Dan Auerbach.
fun. are in the running for all four major field prizes - 'Album of the Year', 'Record of the Year', 'Song of the Year' and 'Best New Artist' - while Ocean is nominated for 'Album of the Year', 'Record of the Year' and 'Best New Artist' at next February's awards.
fun. and Ocean's fellow nominees in the 'Best New Artist' category are Alabama Shakes, Hunter Hayes and The Lumineers.
Mumford & Sons are in the running for 'Album of the Year' for their second longplayer Babel, and also score nominations for 'Best Rock Performance', 'Best Rock Song' and 'Best Short Form Video'.
They are also recognised in the 'Best Song Written For Visual Media' category for 'Learn Me Right', their collaboration with Birdy which is featured in Pixar animated movie Brave.
Four of Jay-Z and West's nominations are for tracks from their collaboration Watch the Throne.
The Black Keys are nominated in five categories as a group, and Auerbach also receives a nomination in his own right for 'Producer of the Year (Non Classical)', where he will face competition including Salaam Remi - producer and friend of the late Amy Winehouse - and Diplo.
Elsewhere, Kelly Clarkson's 'Stronger' is nominated for 'Song of the Year' and 'Record of the Year', and her album of the same name is in the running for the 'Best Pop Album' prize alongside Some Nights by fun., Florence + the Machine's Ceremonials, Maroon 5's Overexposed and The Truth About Love by Pink.
There are also nominations this year for artists including Taylor Swift, Blake Shelton, Ed Sheeran and former 'Best New Artist' winner Esperanza Spalding.
The 55th annual Grammy Awards take place on Sunday, February 10, 2013 at the Staples Centre in Los Angeles. The ceremony will be broadcast live on CBS.
Watch Frank Ocean performing the Grammy-nominated track 'Thinkin' 'Bout You' on Saturday Night Live: