| Hall, Anmer | Anmer Hall | Director | 1928 | 1 | |
| Hemming, Frank | Frank Hemming | Director | 1956 | 1 | |
| Hemphill, Ellen, | Ellen Hemphill | Director | 2011 | 1 | |
| Hoffsommer, June | June Hoffsommer | Director | 1947 | 2 | |
| Homrighous, Mary | Mary Homrighous | Director | 1947 | 2 | |
| Honer, Chris | Chris Honer | Director | 2011 | 1 | |
| Heiberg, Johanne Luise, | Johanne Luise Heiberg | Director | 1870 | 2 | 1 |
| Heiberg, Gunnar, | Gunnar Heiberg | Director | 1885 – 1890 | 9 | |
| Heinrich, Wilhelm Ernst, | Wilhelm Ernst Heinrich | Director | 1889 | 6 | |
| Harding, Jessie, | Jessie Harding | Director | 1895 | 1 | |
| Heine, Dr. Carl, | Carl Heine (Dr. Carl Heine) | Director | 1896 – 1899 | 54 | |
| Hagin, Heinrich, | Heinrich Hagin | Director | 1903 | 2 | |
| Hagemann, Carl, | Carl Hagemann | Director | 1910 | 2 | |
| Heller-Halberg, Friedrich, | Friedrich Heller-Halberg | Director | 1912 | 1 | |
| Hellmer, Arthur, | Arthur Hellmer | Director | 1914 | 2 | |
| Herbert, Eugen, | Eugen Herbert | Director | 1923 | 1 | |
| Held, Ernst, | Ernst Held | Director | 1927 | 1 | |
| Hartung, Gustav, | Gustav Hartung | Director | 1932 | 1 | |
| Henze, Herbert, | Herbert Henze | Director | 1936 | 2 | |
| Heinle, Lutz, | Lutz Heinle | Director | 1941 | 1 | |
| Haufe, Heinz, | Heinz Haufe | Director | 1942 | 1 | |
| Hahn, Erwin, | Erwin Hahn | Director | 1929 | 2 | |
| Hedberg, Karl, | Karl Hedberg | Director | 1901 – 1907 | 5 | |
| Heiberg, Anton, | Anton Heiberg | Director | 1905 | 2 | |
| Høegh, Thomas, | Thomas Høegh | Director | 1991 – 2009 | 12 | |
| Hedemann, Berit, | Berit Hedemann | Director | 1992 | 1 | |
| Hellesøy, Svein, | Svein Hellesøy | Director | 2002 | 1 | |
| Heijermans, Herman, | Herman Heijermans | Director | 1916 | 2 | |
| Hofman, Jerži | Jerži Hofman | Director | 1970 | 1 | |
| Hiatt, Bernard | Bernard Hiatt | Director | 1977 | 1 | |
| Hasnain, Arif | Arif Hasnain | Director | 1977 | 1 | |
| Holt, Louise | Louise Holt | Director | 1928 | 1 | |
| Haspel, Dieter | Dieter Haspel | Director | 1975 | 2 | |
| Hornby, Richard | Richard Hornby | Director | 1975 | 1 | |
| Hjelm, Fred | Fred Hjelm | Director | 1974 – 1992 | 3 | |
| Hopkins, Bernard | Bernard Hopkins | Director | 1978 | 2 | |
| Haugen, Ralph | Ralph Haugen | Director | 1951 – 1972 | 3 | |
| Hancke, Oswald | Oswald Hancke | Director | 1898 | 1 | |
| Hussein, Waris | Waris Hussein | Director | 1972 | 1 | |
| Hoomans, Elise | Elise Hoomans | Director | 1979 | 1 | |
| Hahn, Georg | Georg Hahn | Director | 1973 | 1 | |
| Hahn, Annegret | Annegret Hahn | Director | 1979 | 1 | |
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