| Composer | Title | Year | Pages & duration |
| Hair, Graham (1943-) | Carmina sibyllarum for soprano, two mezzo sopranos, flute, cello, organ & percussion | ||
| Hames, Richard David (1945-) | Orgelwerk: Processional (requires two assistants) | 1980 | 23p. 20m. |
| Sonata Op. 29 | |||
| Hamnes, David Scott (1971-) | Til Anikó | 1997 | 3p. 3m. |
| Til LAACH for organ and clarinet | 2000 | 8p. 5m. | |
| Hannan, Michael (1949-) | Island song for organ, percussion & recorders | 1983 | 8p. 3m. |
| Hanson, Raymond C. (1913-1976) | Sonata for organ in one movement Op. 29 | 1951 | 8p. 8m. |
| Wedding march | 1956 | 2p. 4m. | |
| Three preludes | 1963 | 6p. 7m. | |
| Cantata The Lord reigneth for contralto, string orchestra & organ (with independent organ part) | 1969 | 29p. | |
| Hardy, Lance A. (1907-1993) | Introduction and fugue | c. 1930 | 6m. |
| Fugue in A flat | 1926 | ||
| Harper, Bruce W. (1950-) | Pontifical introit | 1973 | 2p. 1m. |
| Fanfares for organ | 1974 | 4p. 2m. | |
| Hart, Fritz Bennicke (1874-1949) | Fantasia in g minor | 1912 | |
| Three pieces for organ solo Melody Processional Allegretto |
1912 | ||
| Interlude | 1940 | ||
| Wedding march (Also arr. for orchestra as Triumphal march) | 1948 | ||
| Hemans, Michael (1929-1980) | Dialogue, fughetta and toccatina on a traditional Australian air | 13p. 4m. | |
| Henderson, Moya (1941-) | Sacred site for organ & tape i Strong with much feeling ii Virtuosic iii Plangent iv Boisterous v Trancendent vi Flamboyant vii Fast and furious |
1983 | 21p. 13m. |
| Reef I, II & III | 1988 | 23p. 16m. | |
| Hille, Stuart A. (1956-) | Three works for organ Op. 18 | 1975 | 14p. 10m. |
| Hind, John (1916-1984) | Choral fanfare for organ | 1975 | 4p. 3m. |
| Hindson, Matthew (1968 -) | Prelude; Easter Monday | 1988 | 2p. 3m. |
| Hogan, John (1946-) | Archbishop's fanfare | 1975 | 1p. 1m. |
| Our Lady of Victories fanfare | 1975 | 2p. 1m. | |
| Toccata | 1979 | 4p. 4m. | |
| Pange lingua | 1979 | 2p. 4m. | |
| Intrada | 1979 | 1p. 2m. | |
| Chorale prelude on "O Mary of graces" | 1979 | 2p. 4m. | |
| Introduction and toccata | 1995 | 10p. 6m. | |
| Meditation | 1997 | 3p. 5m. | |
| Toccata "Sub tuum" | 1999 | 7p. 5m. | |
| Holland, Dulcie (1913-2000) | With a gladsome mind | 6p. 4m. | |
| Complaint | 4m. | ||
| Two salutations for organ i Peace be with you ii Halleluia |
1965 | 2p.5p. | |
| Chorale in d minor | 1969 | 3p. | |
| Joy cometh in the morning | 1974 | 5p. 4m. | |
| Twilight piece | 1974 | 3p. 3m. | |
| Soliloquy on "Tonus peregrinus" | 1974 | 3p. 4m. | |
| Evening hymn for organ & French horn | 1974 | 2p. | |
| Episode for French horn & organ | 1975 | 5p. | |
| Joyful departure | 1977 | 7p. 6m. | |
| Complaint | 1977 | 4p. | |
| Fanfare | 1977 | 2p. 2m. | |
| O magnum mysterium | 1977 | 3p. | |
| Processional | 1977 | 3p. | |
| Verset | 1977/1985 | 4p. 3m. | |
| Meditations of Mary | 1978 | 6p. 5m. | |
| Hymn prelude for Lent | 1978 | 2p. | |
| Vespers | 1978 | 2p. | |
| Cradle song | 1978 | 4p. | |
| Tuba tune | 1978 | 2p. | |
| Organ toccata in the baroque style | 1986 | 5p. 4m. | |
| Arioso | 1997 | 5p. 5m. | |
| Towards evening | 1997 | 7p. 6m. | |
| Holley, Alan | White Island for trumpet & organ | 17p. 14m. | |
| Hollier, Donald (1934-) | Improvisation on "Veni Immanuel" | 1964 | 13p. |
| Sonata for organ | 1966 | 32p. | |
| Concerto for organ & eighteen strings | 1966 | 66p. | |
| Improvisation on "Old 123rd" | 1969 | 20p. | |
| Improvisation on "Old 100th" | 1971 | ||
| Improvisation on "Old 124th" | 1971 | 18p. | |
| Improvisation on "Monks Gate" | 1972 | 16p. | |
| Occasional music for the churches of Canberra Prelude For St Andrew's Duntroon I Duntroon II For St Christopher's Postlude |
1973 | 14p. | |
| The seven last words of Our Lord from the cross (requires one assistant) | 1975 | 33p. | |
| Improvisation on "St Denio" | 1976 | 17p. | |
| Improvisation on "Vox dilecti" for organ duet | 1979 | 16p. | |
| Horsley, Charles F. (1822-1876) | March | 1866 | 3p. |
| Hooke, John M. (1946-) | Nadir to Zenith | 1975 | |
| Mass for the holy name of Jesus | 1984 | ||
| Howard, Leslie J. (1948-) | Moto di gioia: Postludium | ||
| Preghiera | |||
| Huenerbein, Charles | Air from Music for the ceremonies of the Masonic order arr. A. J. Drewe | 1891 | 2p. 3m. |
| Hughes, William | Motet in three parts | ||
| Humble, Keith (1927-1995) | Arcade I for organ, percussion & tape | 1968 | |
| Statico I for organ & two synthesisers, commissioned by S. de Pieri for MOH | 1970 | ||
| Statico II | 1971 | ||
| Paraphrase "In five" & Mass | 1971 | 11m. | |
| Music for organ and brass commissioned by S. de Pieri for MOH | 1974 | ||
| Hutchens, Frank (1892-1965) | Song of victory | ||
| Hyde, Miriam (1913-) | Chorale in d minor | 1929 rev. 1969 | 3p. 5m. |
| Bridal entry and wedding march | 1973 | 5p. | |
| Prelude in B flat | 1926 | 2m. |