| Year | Category | Nominated work | Result | Ref. |
|---|
| 1958 | Album of the Year | The Music from Peter Gunn | Won | [14] |
| Best Performance by an Orchestra | Nominated |
| Best Arrangement | Won |
| Best Original Cast Album (Broadway or TV) | Nominated |
| 1959 | Album of the Year | More Music from Peter Gunn | Nominated |
| Best Performance by an Orchestra | Nominated |
| Best Jazz Performance – Group | Nominated |
| Best Musical Composition First Recorded and Released in 1958 (Over 5 Minutes Duration) | Nominated |
| Best Soundtrack Album – Background Score from a Motion Picture or Television | Nominated |
| Best Arrangement | Nominated |
| 1960 | "Mr. Lucky" | Won |
| Best Performance by an Orchestra | Won |
| Best Performance by a Band for Dancing | The Blues and the Beat | Nominated |
| Best Jazz Performance Large Group | Won |
| Best Sound Track Album or Recording of Music Score from Motion Picture or Television | Mr. Lucky | Nominated |
| 1961 | Album of the Year (Other Than Classical) | Breakfast at Tiffany's: Music from the Motion Picture | Nominated |
| Record of the Year | "Moon River" | Won |
| Song of the Year | Won |
| Best Arrangement | Won |
| Best Performance by an Orchestra – for Dancing | Mr. Lucky Goes Latin | Nominated |
| Best Performance by an Orchestra – for Other Than Dancing | Breakfast at Tiffany's: Music from the Motion Picture | Won |
| Best Sound Track Album or Recording of Score from Motion Picture or Television | Won |
| 1962 | Best Instrumental Arrangement | "Baby Elephant Walk" | Won |
| Best Instrumental Theme | Nominated |
| Best Original Jazz Composition | "The Sounds of Hatari!" | Nominated |
| Best Performance by an Orchestra or Instrumentalist with Orchestra – Primarily Not Jazz or for Dancing | Hatari! Music from the Paramount Motion Picture Score | Nominated |
| 1963 | Record of the Year | "Days of Wine and Roses" | Won |
| Song of the Year | Won |
| Best Background Arrangement (Behind Vocalist or Instrumentalist) | Won |
| Best Performance by a Chorus | "Charade" | Nominated |
| Best Performance by an Orchestra or Instrumentalist with Orchestra – Primarily Not Jazz or for Dancing | Our Man in Hollywood | Nominated |
| 1964 | Album of the Year | The Pink Panther | Nominated |
| Song of the Year | "Dear Heart" | Nominated |
| Best Performance by a Chorus | Nominated |
| Best Instrumental Arrangement | "The Pink Panther Theme" | Won |
| Best Instrumental Composition (Other Than Jazz) | Won |
| Best Instrumental Performance – Non-Jazz | Won |
| Best Original Score Written for a Motion Picture or Television Show | The Pink Panther | Nominated |
| 1965 | Best Instrumental Performance – Non-Jazz | The Great Race | Nominated |
| Best Performance by a Chorus | Dear Heart and Other Songs about Love | Nominated |
| 1966 | Henry Mancini Presents the Academy Award Songs | Nominated |
| Best Instrumental Theme | "Arabesque" | Nominated |
| Best Instrumental Arrangement | Nominated |
| Best Original Score Written for a Motion Picture or Television Show | Arabesque | Nominated |
| 1969 | Record of the Year | "Love Theme from Romeo and Juliet" | Nominated |
| Best Instrumental Arrangement | Won |
| Best Contemporary Instrumental Performance | Nominated |
| Best Original Score Written for a Motion Picture or a Television Special | Me, Natalie | Nominated |
| 1970 | Best Instrumental Arrangement | "Theme from Z" | Won |
| Best Contemporary Instrumental Performance | "Theme from Z and Other Film Music" | Won |
| Best Instrumental Composition | "Love Theme from Sunflower" | Nominated |
| Best Original Score Written for a Motion Picture or a Television Special | Darling Lili | Nominated |
| 1971 | Best Pop Instrumental Performance | "Theme from Love Story" | Nominated |
| 1972 | Best Instrumental Arrangement | "Theme from The Mancini Generation" | Nominated |
| Best Instrumental Composition | "Brass on Ivory" | Nominated |
| Best Pop Instrumental Performance by an Arranger, Composer, Orchestra and/or Choral Leader | Brass on Ivory | Nominated |
| 1975 | Album of Best Original Score Written for a Motion Picture or a Television Special | The Return of the Pink Panther | Nominated |
| 1976 | Best Instrumental Arrangement | "The Disaster Movie Suite" | Nominated |
| Best Instrumental Composition | "The White Dawn" | Nominated |
| 1978 | Album of Best Original Score Written for a Motion Picture or a Television Special | Revenge of the Pink Panther | Nominated |
| Best Pop Instrumental Performance | "The Pink Panther Theme ('78)" | Nominated |
| 1980 | "Ravel's Boléro" | Nominated |
| 1982 | Best Album of Original Score Written for a Motion Picture or Television Special | Victor/Victoria | Nominated |
| 1983 | Best Instrumental Composition | "The Thorn Birds Theme" | Nominated |
| 1984 | Best Arrangement on an Instrumental | "Cameo for Flute... For James" | Nominated |
| 1987 | Best Instrumental Arrangement Accompanying Vocal(s) | "It Might as Well Be Spring" | Nominated |
| Best Instrumental Composition | "The Blues in Three" | Nominated |
| Best Album of Original Instrumental Background Score Written for a Motion Picture or Television | The Glass Menagerie | Nominated |
| 1988 | Best Instrumental Arrangement Accompanying Vocal(s) | "Volare" | Nominated |
| Best Arrangement on an Instrumental | "Suite from The Thorn Birds" | Nominated |
| 1990 | "Monster Movie Music Suite" | Nominated |
| 1991 | "The Untouchables" | Nominated |
| 1995 | Lifetime Achievement Award | — | Won | [15] |
| 1999 | Grammy Hall of Fame | "Moon River" | Inducted | [16] |
| 2001 | The Pink Panther | Inducted |