| Hoare, Eileen | Eileen Hoare | Director | 2002 | 1 | 1 |
| Horváth, Á. | Á. Horváth | Director | 1925 - 1928 | 2 | |
| Hellmann, Reinhard | Reinhard Hellmann | Director | 1988 - 1994 | 2 | |
| Hachmann, Cord | Cord Hachmann | Director | 1890 - 1897 | 7 | 1 |
| Hagensen, Henrik | Henrik Hagensen | Director | 2006 | 1 | |
| Hagerman, Helge | Helge Hagerman | Director | 1956 | 1 | |
| Hall, Violet | Violet Hall | Director | 1943 - 1944 | 3 | |
| Hampson, Linda | Linda Hampson | Director | 2007 | 1 | |
| Hanau, John | John Hanau | Director | 1956 | 1 | |
| Hård, Karin | Karin Hård | Director | 1999 | 1 | |
| Hartl, Václav | Václav Hartl | Director | 1956 | 1 | 1 |
| Hathazy, Peter | Peter Hathazy | Director | 1993 - 1996 | 3 | |
| Hatry, Michael | Michael Hatry | Director | 1974 | 1 | |
| Heinzelmann, Markus | Markus Heinzelmann | Director | 2004 | 1 | 1 |
| Henkel, Karin | Karin Henkel | Director | 1997 - 2015 | 5 | 1 |
| Hersov, Gregory | Gregory Hersov | Director | 1987 - 2013 | 3 | |
| Herz, Juraj | Juraj Herz | Director | 1973 | 1 | |
| Hevesi, Sándor | Sándor Hevesi | Director | 1905 - 1928 | 4 | 1 |
| Hicks, Israel | Israel Hicks | Director | 2005 | 1 | |
| Hilpert, Heinz | Heinz Hilpert | Director | 1928 - 1943 | 6 | |
| 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 | |
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