As a child, Graf learned the violin and the piano. He studied at the Musikhochschule in Graz, Austria, and graduated with diplomas in piano and conducting. He also participated in conducting master classes with Franco Ferrara, Sergiu Celibidache and Arvīds Jansons. He received a state scholarship at the Leningrad Conservatory with Arvid Jansons. For the season 1975/1976 Graf was music director of the Iraqi National Symphony Orchestra in Baghdad. After winning the Karl Böhm conductor's competition in 1979, he made his debut at the Vienna State Opera in 1981 with Stravinsky's Petrouchka. Since 1995, he has collaborated with many major American orchestras, including the Boston Symphony, Cleveland Orchestra, New York Philharmonic and Philadelphia Orchestra.
Graf was music director of the Mozarteum Orchestra of Salzburg from 1984 to 1994, where he recorded the complete symphonies and other works by Mozart. From 1995 to 2003, Graf was music director of the Calgary Philharmonic Orchestra. He was also music director of the Orchestre National Bordeaux Aquitaine, France, from 1998 to 2004.
Graf first conducted the Houston Symphony in 2000, and became its music director in 2001. He made his Carnegie Hall conducting debut with the Houston Symphony in January 2006. In September 2009, the orchestra announced the extension of Graf's contract as music director through the 2012/2013 season, and the conclusion of his Houston tenure at that time, upon which Graf is to take the title of Conductor Laureate. He has been an artist-in-residence at the Shepherd School of Music, Rice University. On 2 December 2012 Graf was honoured by the Bruckner Society of America with the Kilenyi Medal of Honor for his performances of the Bruckner's Symphonies 3-4 and 6-9 including the sketches to Finale of the 9th, as well as the Mass No. 2 and the Te Deum.
From 2013 to 2015, Graf was professor for orchestral conducting at Salzburg's Mozarteum University. In 2017, he will perform at the festivals at Tanglewood and Aspen.
In 2018, he won a Grammy award for the recording of Alban Berg's Wozzeck with Anne Schwanewilms, Roman Trekel and the Houston Symphony.
In private life, Graf is known as a wine connoisseur. He and his wife Margarita have a daughter, Anna.
- 2017: Alban Berg: Wozzeck. Roman Trekel, Anne Schwanewilms, Houston Symphony (Naxos). ECHO Klassik Prize 2017 for best 20th/21st century opera recording and Grammy 2018 award for best opera recording.
- 2014: Carl Orff: Carmina Burana. Sarah Tynan, Andrew Kennedy, Rodion Pogossow, London Philharmonic Orchestra & Choir, Trinity Boys Choir (LPO)
- 2012: Paul Hindemith: Works for Viola and Orchestra (Der Schwanendreher, Trauermusik, Kammermusik Nr. 5 op. 36 Nr. 4, Konzertmusik op. 48a. First recording of early version). Tabea Zimmermann, Deutsches Symphonie-Orchester Berlin (Myrios)
- 2010: The Planets. An HD Odyssey (DVD with film material from NASA, Video by Duncan Copp). Music: Gustav Holst: The Planets. Houston Symphony (HS Label)
- 2009: Gustav Mahler: Das Lied von der Erde. Jane Henschel, Gregory Kunde, Houston Symphony (Naxos)
- 2007: Alexander Zemlinsky: Lyrische Symphonie op. 18, Alban Berg: Three pieces from the Lyric Suite (version for string orchestra). Twyla Robinson, Roman Trekel, Houston Symphony (Naxos)
- 2007: George Gershwin: An American in Paris, Concerto in F, Porgy and Bess, A Symphonic Picture (arr. Richard Bennett). Jon Kimura Parker, Houston Symphony (HS Label)
- 2006: Johann Strauss jr.: Overtures, waltzes, polkas. Houston Symphony Orchestra & Chorus (HS Label)
- 2004: Béla Bartók: The Wooden Prince, Igor Strawinski: Divertimento (from Le Baiser de la Fée). Houston Symphony (Koch International)
- 2004: Wolfgang Amadeus Mozart: Requiem K 626, Symphony C-Dur K 338, Sinfonia Concertante for violin, viola and cello K Anh. 104 (Fragment, orch. Hans Graf). Heidi Grant Murphy, Jane Gilbert, Stanford Olsen, Nathan Berg, Eric Halen, Wayne Brooks, Brinton Smith, Houston Symphony Orchestra & Chorus (HS Label, 2 CDs)
- 2004: Anton Bruckner: Symphonie Nr. 4 E flat major. Houston Symphony (HS Label)
- 2000–2004: Henri Dutilleux: Orchestral works: Symphony Nr. 2, Métaboles, The Shadows of Time, Symphony Nr. 1, Tout un monde lointain… (cello concerto), Timbres, Espace, Mouvement ou La Nuit Etoilée, L'Arbre des Songes (violin concerto), La Geôle (first recording), Deux Sonnets de Jean Cassou, Mystère de l'Instant (version for large orchestra). Jean Guihen Queyras, Olivier Charlier, François Le Roux, Orchestre National Bordeaux Aquitaine (Arte Nova/Sony, 3 CDs)
- 2001: Darius Milhaud: Saudades do Brazil, Scaramouche for saxophone and orchestra. Heitor Villa-Lobos: Descobrimento do Brazil (Suite 2 & 3). Jeremy Brown, Calgary Philharmonic Orchestra (CBC Records)
- 2001: Carl Orff: Carmina Burana. Christine Brandes, Noel E. Velasco, Stephen Powell, Ford Bend Boys Chorus, Houston Symphony Orchestra & Chorus (HS Label)
- 1998–2000: Franz Schubert: The complete symphonies, 4 overtures. Aarhus Symphony Orchestra (Kontrapunkt, 5 CDs)
- 1999: Gustav Mahler: Symphony Nr. 1 D major (incl. Blumine). Calgary Philharmonic Orchestra (CPO Label)
- 1999: Franz Liszt: Piano concertos Nr. 1 E flat major, Nr. 2 A major, Nr. 3 E flat major (Op. posth., ed. Jerry Rosenblatt), Concerto in the Hungarian style ("Sophie Menter-Konzert", orch. P.I. Tschaikowski). Janina Fialkowska, Calgary Philharmonic Orchestra (CBC Records)
- 1997: Manuel de Falla: Nights in the Gardens of Spain. Isaac Albeniz: Rapsodia Española, Joaquin Turina: Rapsodia Sinfonica, Xavier Montsalvatge: Concierto Breve. Angela Cheng, Calgary Philharmonic Orchestra (CBC Records)
- 1992–1994: Wolfgang Amadeus Mozart: Piano concertos K 271, 414, 456, 459, 466, 467, 482, 488, 491, 503, 537, 595. Éric Heidsieck, Mozarteum Orchester Salzburg (JVC, 6 CDs)
- 1994: Anton Bruckner: Symphony Nr. 8. Mozarteum Orchester Salzburg (VFMO 0894-1/2)
- 1990: Wolfgang Amadeus Mozart: Violin concertos Nr. 1 B flat major K 207, Nr. 2 D major K 211, Adagio for violin and orchestra K 261, Rondos for violin and orchestra K 269 & 373. Benjamin Schmid, Mozarteum Orchester Salzburg (Capriccio)
- 1990: Wolfgang Amadeus Mozart: Concertos for flute and orchestra K 313 & 314, Andante for flute and orchestra in C major K 315, Rondo in D major K Anh. 184. Shigenori Kudo, Mozarteum Orchester Salzburg (NEC Classics)
- 1990: Wolfgang Amadeus Mozart: Dances and Minuets. Mozarteum Orchester Salzburg (Capriccio)
- 1989–1990: Wolfgang Amadeus Mozart: The complete symphonies. Mozarteum Orchester Salzburg (Capriccio, 13 CDs)
- 1989: Ludwig van Beethoven: Piano concertos Nr. 1 C major & No. 4 G major. Maria Tipo, London Symphony Orchestra (EMI)
- 1989: Wolfgang Amadeus Mozart: Concert for flute and harp K 299, Rondo in D major K Anh. 184, Concert for flute in D major K 314, Andante for flute and orchestra in C major K 315. Simion Stanciu, Helga Storck, Mozarteum Orchester Salzburg (Erato)
- 1988: Wolfgang Amadeus Mozart: Marches. Mozarteum Orchester Salzburg (Capriccio)
- 1987: Alexander Zemlinsky: Es war einmal (First recording). Eva Johansson, Kurt Westi, Aage Haugland, Per Arne Wahlgren, Danish National Radio Symphony Orchestra & Chorus (Capriccio)
- 1981: Franz Lehár: Der Rastelbinder (First recording). Fritz Muliar, Elfie Hobarth, Helga Papouschek, Heinz Zednik, Adolf Dallapozza, Wiener Mozart Sängerknaben, ORF Chor, Radio-Symphonieorchester Wien (CPO/WDR/ORF)
- Allan Kozinn (26 January 2006). "An Icy Shostakovich and a Trim Mozart, by Way of Texas". The New York Times. Retrieved 14 August 2007.
- Kevin Shihoten (9 July 2007). "Hans Graf Signs with Houston Symphony Through 2012". Playbill Arts. Retrieved 14 August 2007.
- Tara Dooley (23 September 2009). "Hans Graf takes steps to leave symphony". Houston Chronicle. Retrieved 2 October 2009.
- Hans Graf Receives the Bruckner Society of America's Medal of Honor
- "60th Annual GRAMMY Awards". GRAMMY.com. 2017-11-28. Retrieved 2018-01-28.
- Shelby Hodge (1 June 2006). "Houston Symphony League toasts the maestro". Houston Chronicle. Retrieved 14 August 2007.
- International, MusicWeb. "Berg Wozzeck NAXOS 8.660390-91 [GPJ] Classical Music Reviews: February 2017 - MusicWeb-International". www.musicweb-international.com. Retrieved 2017-07-22.
- "60th Annual GRAMMY Awards". GRAMMY.com. 2017-11-28. Retrieved 2018-01-28.
| Music Director, Mozarteum Orchestra of Salzburg
| Music Director, Orquesta de Euskadi
Gilbert Varga, Mario Venzago
| Music Director, Calgary Philharmonic Orchestra
| Music Director, Orchestre National Bordeaux Aquitaine
| Music Director, Houston Symphony
Dennis Russell Davies
| Professor for orchestral conducting, Mozarteum University of Salzburg