| Song title Bold titles have been released in some form (?) indicates song title unconfirmed (Name) in brackets indicates artist if not credited as ABBA (or Björn & Benny, Agnetha & Frida) | First known recording or performance date (?) indicates date not known or unconfirmed (NR) indicates song not recorded |
| Hades | 24 April 1978 |
| Hamlet III | 31 August 1978 |
| Hamlet III Parts 1 & 2 | 1994 |
| Hamlet 111 Parts 1 & 2 | 1994 |
| Hamlet 3 Parts 1 & 2 | 1994 |
| Happy Birthday To You | 1981 (?) |
| Happy Hawaii | 14 May 1976 |
| Happy Hawaii/Why Did It Have To Be Me (Benny Andersson) | July 2011 |
| Happy New Year | 9 April 1980 |
| Happy New Year – a new togetherness (ABBA The Museum The Choir with Benny Andersson) | December 2020 |
| Happy New Year (Benny Andersson) | March 1987 |
| Happy New Year (Benny Andersson) | December 2013 |
| Happy New Year (Benny Andersson) | Early 2017 |
| Happy New Year (Benny Andersson) | 29 December 2021 |
| Happy New Year (Benny Andersson with Europe) | 31 December 1987 |
| Happy New Year (video edit) | late 1999 |
| Harry | 5 May 1982 |
| Hasta Mañana | 18 December 1973 |
| Hasta Mañana (Benny Anderssons Orkester) | June 2009 |
| Hasta Mañana (Helen Sjöholm) | 2017 |
| Hasta Mañana (Spanish version) | 7 January 1980 |
| Have You Never Been Mellow | 8 May 1978 |
| Hawaii | 26 April 1976 |
| Head Over Heels | 2 September 1981 |
| Head Over Heels (alternate mix) | 2 September 1981 |
| The Heat Is On (Agnetha) | circa 17 January – end March 1983 |
| He Is Your Brother | 17 October 1972 |
| He Is Your Brother (Music for UNICEF) | 9 January 1979 |
| He Is Your Brother (Benny Anderssons Orkester) | 25 July 2019 |
| Hej gamle man! (Björn & Benny) | June 1970 |
| Helan går | 12 April 1978 |
| Help Me Rhonda | 8 May 1978 |
| Here Comes Rubie Jamie | 16 September 1974 |
| Here Comes Rubie Jamie (Terra del Fuego) | 16 September 1974 |
| Here We’ll Stay (Special version) (Frida) | April 1983 |
| Heroes | 24 April 1978 |
| Hey Grand Ol’ Man (Björn) | February 2022 |
| Hey, Hey Helen | 14 September 1974 |
| High High | 1 June 1977 |
| High On Your Love | 3 August 1977 |
| Hit By A Train | 2019 (?) |
| Hold Me Close | 4 February 1980 |
| Hole In Your Soul | 3 August 1977 |
| Hole In Your Soul (movie edit) | 3 August 1977 |
| Hole In Your Soul (Panos Mouzourakis) | 2017 |
| Holiday | 8 May 1978 |
| Honey, Honey | 17 October 1973 |
| Honey, Honey (Amanda Seyfried, Ashley Lilley & Rachel McDowall) | February 2007 |
| Honey, Honey (Benny Anderssons orkester) | March 2006 |
| Honey, Honey (in Swedish) | 30 January 1974 |
| Honey, Honey (Swedish version) | 30 January 1974 |
| Honey-Pie | December 1973 (?) |
| Honeysuckle Rose | 23 October 1974 |
| Horn Per | 25 April 1978 |
| Hou Je Echt Nog Van Mij, Rocking Billy? (Ria Valk) | 1961 |
| Hovas vittne | 18 January 1981 |
| Hung Up (Madonna) | 2005 |
| Hurry | 5 May 1982 |
ABBA Omnibus 