| Name | Dates | Era | Nationality |
|---|---|---|---|
| Hába, Alois | 06/21/1893 - 11/18/1973 | 20th Century | Czech Republic |
| Halévy, Jacques Fromental | 05/27/1799 - 03/17/1862 | Classical | France |
| Haley, Bill | 07/06/1925 - 02/09/1981 | 20th Century | USA |
| Halle, Adam de la | c. 1237 - c. 1287 | Medieval | France |
| Hamlisch, Marvin | 06/02/1944 - 08/07/2012 | 20th Century | USA |
| Hammerschmidt, Andreas | c. 1612 - 10/29/1675 | Baroque | Germany |
| Handel, George Frederic | 02/23/1685 - 04/14/1759 | Baroque | Germany |
| Handl (Gallus), Jacob | 07/03/1550 - 07/18/1591 | Renaissance | Germany |
| Hanson, Howard | 10/28/1896 - 02/26/1981 | 20th Century | USA |
| Harbison, John | 12/20/1938 | 20th Century | USA |
| Harris, Charles Kassell | 05/01/1867 - 12/22/1930 | 20th Century | USA |
| Harris, Roy | 02/12/1898 - 10/01/1979 | 20th Century | USA |
| Harsányi, Tibor | 06/27/1898 - 09/19/1954 | Romantic | Hungary |
| Hasse, Johann Adolf | 03/25/1699 - 12/16/1783 | Baroque | Germany |
| Hassler, Hans Leo | 10/26/1564 - 06/08/1612 | Renaissance | Germany |
| Haydn, Michael | 09/14/1737 - 08/10/1806 | Classical | Austria |
| Haydn, Franz Joseph | 03/31/1732 - 05/31/1809 | Classical | Austria |
| Heiden, Bernard | 08/24/1910 - 04/30/2000 | 20th Century | Italy |
| Heinrich, Anthony Philip | 03/11/1781 - 05/03/1861 | Classical | USA |
| Hellinck, Lupus | c. 1496 - 1541 | Renaissance | Netherlands |
| Henze, Hans Werner | 07/01/1926 - 10/27/2012 | 20th Century | Germany |
| Herbert, Victor August | 02/01/1859 - 05/26/1924 | Romantic | Ireland |
| Hérold , Ferdinand | 01/28/1791 - 01/19/1833 | Classical | France |
| Herrmann, Bernard | 06/29/1911 - 12/24/1975 | 20th Century | USA |
| Hildegard of Bingen, | 1098 - 09/17/1179 | Ancient | Germany |
| Hiller, Johann Adam | 1728 - 1804 | Classical | Germany |
| Hindemith, Paul | 11/16/1895 - 12/28/1963 | 20th Century | Germany |
| Hoffmann, E.T.A. | 01/24/1776 - 06/25/1822 | Romantic | Germany |
| Hofhaimer, Paul | 1459 - 1537 | Renaissance | Germany |
| Holst, Gustav | 1874 - 1934 | Romantic | England |
| Holzbauer, Ignaz | 1711 - 1783 | Baroque | Austria |
| Honegger, Arthur | 03/10/1892 - 11/27/1955 | 20th Century | Switzerland |
| Hopkinson, Francis | 1737 - 1791 | Classical | USA |
| Hothby, John | c. 1410 - 1487 | Renaissance | England |
| Hovhaness, Alan Scott | 03/08/1911 - 06/21/2000 | 20th Century | USA |
| Hummel, Johann Nepomuk | 11/14/1778 - 10/17/1837 | Romantic | Austria |
| Humperdinck, Englebert | 1854 - 1921 | Romantic | Germany |
| Hunfrey, Pelham | 1647 - 1674 | Baroque | England |
| Husa, Karel | 08/07/1921 - 12/14/2016 | 20th Century | Czech Republic |