| Year | Category | Movie | Win/Nominated |
|---|---|---|---|
| 1961 | Best Musical Score | West Side Story (1961) | Win |
| 1956 | Best Musical Score | High Society (1956) | Nominated |
| 1954 | Best Musical Score | Seven Brides For Seven Brothers (1954) | Win |
| 1953 | Best Musical Score | Kiss Me Kate (1953) | Nominated |
| 1951 | Best Musical Score | American in Paris (1951) | Win |