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- Henry Kimball Hadley (1871–1937)
- Richard Hageman (1881–1966)
- Daron Hagen (born 1961)
- Alexei Haieff (1914–1994)
- Adolphus Hailstork (born 1941)
- Roger Lee Hall (born 1942)
- Howard Hanson (1896–1981)
- John Harbison (born 1938)
- Don L. Harper
- Kevin F. Harris (born 1965)
- Roy Harris (1898–1979)
- Victor Harris (1869–1943)
- Lou Harrison (1917–2003)
- Stephen Hartke (born 1952)
- Walter Hartley (born 1927)
- Denise Sherry-Williams Hall (Born 1955?? ish...)
- James Hartway (born 1944)
- Samuel Hazo (born 1966)
- Hubert Klyne Headley (1906–1996)
- Neal Hefti (1922–2008)
- Jake Heggie (born 1961)
- Anthony Philip Heinrich (1781–1861)
- Robert Helps (1928–2001)
- Victor Herbert (1859–1924)
- Bernard Herrmann (1911–1975)
- Michael Hersch (born 1971)
- James Hewitt (1770–1827)
- Sean Hickey (born 1970)
- Jennifer Higdon (born 1962)
- Edward Burlingame Hill (1872–1960)
- Lee Hoiby (1926–2011)
- Oliver Holden (1765–1844)
- James Nathaniel Holland (born 1966)
- Sidney Homer (c. 1864 – 1953)
- Alan Hovhaness (1911–2000)
- James Newton Howard (born 1951)
- Huang Ruo (born 1976)
- Richard Hundley (born 1931)
- Karel Husa (born 1921)
- Henry Holden Huss (1862–1953)
- Jason Kao Hwang (born 1957)
Read more about this topic: List Of American Composers