Steve Kuhn was born on March 24, 1938, in New York City to Hungarian-Jewish immigrants, Stella (née Kaufman) and Carl Kuhn, and grew up in Newton, Massachusetts. At five he began lessons in Boston with Margaret Chaloff, the mother of the baritone saxophonist Serge Chaloff, who taught him a Russian-school approach to the instrument. As a teenager he sat in at Boston clubs alongside Chet Baker, Coleman Hawkins, trombonist Vic Dickenson and Serge Chaloff himself. He studied at Harvard, where his taste for jazz made him an outlier among the music majors, and in 1959 attended the School of Jazz in Lenox, Massachusetts. There he met Ornette Coleman and Don Cherry and the arranger Gary McFarland, and learned from a faculty that included Bill Evans, George Russell, Gunther Schuller and members of the Modern Jazz Quartet.

He moved to New York and joined the trumpeter Kenny Dorham's group, recording Jazz Contemporary (Time, 1960). In 1960 he became the first pianist in John Coltrane's new quartet during its stand at the Jazz Gallery, a stay that lasted only briefly before McCoy Tyner took the piano chair for good. That November he recorded a trio session with the bassist Scott LaFaro and the drummer Pete La Roca, released only in 2005 as 1960. In 1961 he was the pianist on Stan Getz's Focus, a Verve album of string writing by Eddie Sauter, and the same year he played on Getz's Recorded Fall 1961, a quartet date with the valve trombonist Bob Brookmeyer. Through the mid-1960s he worked with Art Farmer, recording Sing Me Softly of the Blues for Atlantic in 1965, and with La Roca on Basra for Blue Note, which also featured Joe Henderson. His own trio with the bassist Steve Swallow and La Roca recorded Three Waves (Contact, 1966). The October Suite, recorded in 1966 and issued on Impulse! in 1967, is a set of pieces for strings, woodwinds and rhythm section that Gary McFarland composed for him, and he also played in Oliver Nelson's quartet with Ron Carter on Sound Pieces (Impulse!).

From 1967 to 1971 Kuhn lived in Stockholm, leading his own trio around Europe. With the bassist Palle Danielsson and the drummer Jon Christensen he recorded Watch What Happens! for MPS in 1968, and he also appeared on Alto Summit (MPS, 1968), a date featuring the altoists Lee Konitz and Phil Woods, Pony Poindexter and Leo Wright. After returning to New York in 1971 he formed a quartet and recorded for Buddah and Cobblestone, including the 1972 live set from New York. Then came a long run of albums for ECM, produced by Manfred Eicher: the solo Ecstasy and the quartet Trance with Swallow, Jack DeJohnette and the percussionist Sue Evans in November 1974, followed by Motility (1977) and Non-Fiction (1978) under the group name Steve Kuhn and Ecstasy, with the saxophonist Steve Slagle and the bassist Harvie S. In 1979 he added the singer Sheila Jordan to that quartet for Playground (1980) and Last Year's Waltz (1982).

In the 1980s and 1990s Kuhn settled into the piano trio as his main vehicle, with Ron Carter and Al Foster on the live Life's Magic and The Vanguard Date (both from March 1986), then with the bassist David Finck and the drummers Lewis Nash and Joey Baron. He returned to ECM with Remembering Tomorrow (1996), made a run of albums for Reservoir with Finck and Billy Drummond between 1998 and 2000, and recorded steadily for the Japanese label Venus from 1997 to 2010. Promises Kept (ECM, 2004), recorded in 2000, set his own compositions for trio and a fifteen-piece string ensemble conducted by Carlos Franzetti. Live at Birdland (Blue Note, 2007) paired him again with Carter and Foster, and Mostly Coltrane (ECM, 2009), with the saxophonist Joe Lovano, looked back at his short time in Coltrane's band.

His later records were trio dates with Swallow and Joey Baron: Wisteria (ECM, 2012), At This Time... (Sunnyside, 2016) and To and From the Heart (Sunnyside, 2018). He also made Break of Day (2014) with the Norwegian singer Karin Krog, and in August 2017 played with Krog and the saxophonist John Surman at the Oslo Jazz Festival. He wrote "The Saga of Harrison Crabfeathers," which became a standard. Kuhn announced in late 2022 that he had retired from touring.

AllMusic calls Kuhn the quintessential post-bop pianist, thoroughly modernist in approach. His technique grew out of the classical, Russian-school lessons of his Boston teacher, and in his early years he was known as an avant-garde player, working in the 1960s with Steve Swallow and La Roca on records that were widely noted. Chamber textures run through his larger projects, from Gary McFarland's The October Suite to his own string album Promises Kept, and he wrote the standard "The Saga of Harrison Crabfeathers." Ballads and singers are a second thread: his work with Sheila Jordan and Karin Krog is central to his catalogue, and his long partnership with Swallow ran from the 1960s to 2018. Dan Morgenstern, then director of the Institute of Jazz Studies at Rutgers, said in 2009 that Kuhn was one of the finest pianists out there and should have a bigger name.