1st Annual Grammy Awards

General

Record of the Year

• "Nel Blu Dipinto di Blu (Volare)" – Domenico Modugno
• "Catch A Falling Star" – Perry Como
• "Fever" – Peggy Lee
• "The Chipmunk Song" – David Seville And The Chipmunks
• "Witchcraft" – Frank Sinatra

Album of the Year

• The Music from Peter Gunn – Henry Mancini
• Tchaikovksy: Concerto No. 1 In B-Flat Minor, Op. 23 – Van Cliburn
• Ella Fitzgerald Sings the Irving Berlin Song Book – Ella Fitzgerald
• Come Fly with Me – Frank Sinatra
• Only The Lonely – Frank Sinatra

Song of the Year

• "Nel Blu Dipinto di Blu (Volare)" – Franco Migliacci and Domenico Modugno, songwriters (Domenico Modugno)
• "Catch A Falling Star" – Lee Pockriss and Paul Vance, songwriters (Perry Como)
• "Gigi" – Alan Jay Lerner and Frederick Loewe, songwriters (Vic Damone)
• "Fever" – Eddie Cooley and Johnny Davenport, songwriters (Peggy Lee)
• "Witchcraft" – Cy Coleman and Carolyn Leigh, songwriters (Frank Sinatra)

Children's

• Best Recording for Children
  • Ross Bagdasarian Sr. for "The Chipmunk Song (Christmas Don't Be Late)" performed by Ross Bagdasarian Sr. as "David Seville and the Chipmunks"

Comedy

• Best Comedy Performance
  • Ross Bagdasarian, Sr. for "The Chipmunk Song", performed by Ross Bagdasarian Sr. as "David Seville and the Chipmunks"

Composing and arranging

• Best Musical Composition First Recorded and Released in 1958 (over 5 minutes duration)
  • Nelson Riddle (composer) for "Cross Country Suite"
• Best Arrangement
  • Henry Mancini (arranger & artist) for The Music from Peter Gunn

Country

• Best Country & Western Performance
  • The Kingston Trio for "Tom Dooley"

Jazz

• Best Jazz Performance, Individual
  • Ella Fitzgerald for Ella Fitzgerald Sings the Duke Ellington Songbook
• Best Jazz Performance, Group
  • Count Basie for Basie

Musical show

• Best Original Cast Album (Broadway or TV)
  • Meredith Willson (composer) & the original cast with Robert Preston, Barbara Cook, David Burns, Eddie Hodges, Pert Kelton & Helen Raymond for The Music Man
• Best Sound Track Album, Dramatic Picture Score or Original Cast
  • André Previn & the original cast for Gigi (Original Motion Picture Soundtrack)

Packaging and notes

• Best Album Cover Photography
  • Frank Sinatra for Frank Sinatra Sings for Only the Lonely

Pop

• Best Vocal Performance, Female
  • Ella Fitzgerald for Ella Fitzgerald Sings the Irving Berlin Songbook
• Best Vocal Performance, Male
  • Perry Como for "Catch a Falling Star"
• Best Performance by a Vocal Group or Chorus
  • Keely Smith & Louis Prima for "That Old Black Magic"
• Best Performance by a Dance Band
  • Count Basie for Basie
• Best Performance by an Orchestra
  • Billy May for Billy May's Big Fat Brass

Production and engineering

• Best Engineered Record - Non-Classical
  • Ted Keep (engineer) for "The Chipmunk Song" performed by David Seville
• Best Engineered Record (Classical)
  • Sherwood Hall III (engineer), Laurindo Almeida & Salli Terri for Duets with Spanish Guitar

R&B

• Best Rhythm & Blues Performance
  • "Tequila"-The Champs

Spoken

• Best Performance, Documentary or Spoken Word
  • Stan Freberg for The Best of the Stan Freberg Shows