| Best Music, Score (nom) | Lost Horizon | 1937 |
| Best Music, Scoring (nom) | Mr. Smith Goes to Washington | 1939 |
| Best Music, Scoring of a Dramatic or Comedy Picture (nom) | The Corsican Brothers | 1942 |
| Best Music, Scoring of a Dramatic or Comedy Picture (nom) | The Moon and Sixpence | 1943 |
| Best Music, Scoring of a Dramatic or Comedy Picture (nom) | The Bridge of San Luis Rey | 1944 |
| Best Music, Scoring of a Dramatic or Comedy Picture (nom) | Champion | 1949 |
Best Music, Scoring of a Dramatic or Comedy Picture (win)  |
High Noon | 1952 |
| Best Music, Song (win) |
High Noon (Do Not Forsake Me, Oh, My Darlin') Aware shared with Ned Washington (lyrics) |
1952 |
| Best Music, Scoring of a Dramatic or Comedy Picture (win) |
The High and the Mighty | 1954 |
| Best Music, Song (nom) | The High and the Mighty Nomination shared with Ned Washington (lyrics) |
1954 |
| Best Music, Scoring of a Dramatic or Comedy Picture (nom) | Giant | 1956 |
| Best Music, Song (nom) | Friendly Persuasion (Thee I Love) Nomination shared with Paul Frencis Webster (lyrics) |
1956 |
| Best Music, Song (nom) | Wild Is the Wind Nomination shared with Ned Washington (lyrics) |
1957 |
| Best Music, Scoring of a Dramatic or Comedy Picture (win) |
The Old Man and the Sea | 1958 |
| Best Music, Song (nom) | Strange Are The Ways Of Love (from "The Young Land") Nomination shared with Ned Washington (lyrics) |
1959 |
| Best Music, Scoring of a Dramatic or Comedy Picture (nom) | The Alamo | 1960 |
| Best Music, Song (nom) | The Green Leaves Of Summer (from "The Alamo") Nomination shared with Paul Frencis Webster (lyrics) |
1960 |
| Best Music, Scoring of a Dramatic or Comedy Picture (nom) | The Guns of Navarone | 1961 |
| Best Music, Song (nom) | Town Without Pity Nomination shared with Ned Washington (lyrics) |
1961 |
| Best Music, Scoring of a Dramatic or Comedy Picture (nom) | 55 Days at Peking | 1963 |
| Best Music, Song (nom) | So Little Time (Peking Theme) Nomination shared with Paul Frencis Webster (lyrics) |
1963 |
| Best Music, Scoring of a Dramatic or Comedy Picture (nom) | The Fall of the Roman Empire | 1964 |
| Best Music, Scoring of a Dramatic or Comedy Picture (nom) | Tchaikovsky | 1971 |