| Hilsdorf, Dietrich | Dietrich Hilsdorf | Director | 2001 - 2016 | 2 | |
| Hirschfeld, Kurt | Kurt Hirschfeld | Director | 1959 | 1 | |
| Hohenemser, Henri | Henri Hohenemser | Director | 1974 - 1977 | 2 | |
| Holderness, Rebecca | Rebecca Holderness | Director | 2001 | 1 | |
| Holmes, Debby | Debby Holmes | Director | 2000 | 1 | |
| Holzhäuser, Hans-Peter | Hans-Peter Holzhäuser | Director | 1970 | 1 | |
| Horne, Michael | Michael Horne | Director | 1990 | 1 | |
| Howard, John E. | John E. Howard | Director | 1930 | 1 | |
| Hühn, Matthias | Matthias Hühn (Matthias Huhn) | Director | 2007 - 2008 | 2 | 1 |
| Huisman, Jacques | Jacques Huisman | Director | 1984 | 1 | |
| Holst, Hans Peter | Hans Peter Holst | Director | 1879 - 1906 | 17 | 1 |
| Heissan Jr., Joseph A. | Joseph A. Heissan Jr. | Director | 1994 - 1998 | 2 | |
| Harwood, Frank | Frank Harwood | Director | 1937 - 1956 | 2 | |
| Hyvärinen, Teija | Teija Hyvärinen | Director | 2006 | 1 | |
| Hartnett, Terence | Terence Hartnett | Director | 2002 | 1 | |
| Hansen, Steen Haakon | Steen Haakon Hansen | Director | 1988 | 1 | |
| Hollaender, Felix | Felix Hollaender | Director | 1917 - 1918 | 4 | 1 |
| Hong, Hye-sung | Hye-sung Hong | Director | 1934 | 1 | |
| Hall, Anmer | Anmer Hall | Director | 1928 | 1 | 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 | 2 |
| Heiberg, Gunnar | Gunnar Heiberg | Director | 1885 - 1918 | 9 | 1 |
| Heinrich, Wilhelm Ernst | Wilhelm Ernst Heinrich | Director | 1889 - 1901 | 6 | |
| Harding, Jessie | Jessie Harding | Director | 1895 | 1 | |
| Heine, Dr. Carl | Carl Heine (Dr. Carl Heine) | Director | 1896 - 1918 | 54 | 1 |
| Hagin, Heinrich | Heinrich Hagin | Director | 1903 - 1904 | 2 | |
| Hagemann, Carl | Carl Hagemann | Director | 1910 - 1911 | 2 | |
| Heller-Halberg, Friedrich | Friedrich Heller-Halberg | Director | 1912 | 1 | |
| Hellmer, Arthur | Arthur Hellmer | Director | 1914 - 1915 | 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 - 1938 | 2 | |
| Heinle, Lutz | Lutz Heinle | Director | 1941 | 1 | |
| Haufe, Heinz | Heinz Haufe | Director | 1942 | 1 | |
| Hahn, Erwin | Erwin Hahn | Director | 1929 - 1947 | 2 | |
| Hedberg, Karl | Karl Hedberg | Director | 1901 - 1918 | 5 | |
| Heiberg, Anton | Anton Heiberg | Director | 1905 - 1907 | 2 | |
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