Barraqué was born in Puteaux. He studied in Paris with Jean Langlais and Olivier Messiaen and through Messiaen became interested in serialism.
It is thought that Barraqué destroyed many of his early works (at any rate, scores for them have not been found), leaving his Piano Sonata, completed in 1952, as his earliest surviving work. It is a large piece, lasting almost an hour, and is divided into two conncted sections, roughly equal in length. The texture of the work is often compared to Pierre Boulez, though the overall structure is quite different to anything Boulez has written, and more closely resembles the late sonatas of Ludwig van Beethoven (because of its sheer size and difficulty, it is sometimes compared to Beethoven's Piano Sonata No. 29, the Hammerklavier). The sonata was premiered by Yvonne Loriod.
Barraqué then produced his only electronic piece, the Etude (1954), made at Pierre Schaeffer's studio. He then planned a large scale piece, or rather collection of pieces, based on Hermann Broch's novel The Death of Virgil, a book which Barraqué's friend and lover Michel Foucault recommended to him. He completed three of the projected parts, ... au dela du hasard (1959); Chant aprés chant (1966); and Le temps restitué (1957, orchestrated 1968), before his death. Fragments of the other parts also exist.
Barraqué also wrote a Concerto in 1968, which is related to The Death of Virgil, but not actually part of that cycle. The only other extant piece by Barraqué is Sequence (1954) for soprano and ensemble.
Barraqué's use of tone rows in his work is quite distinctive. Rather than using a single tone row for an entire piece, as Anton Webern did, or using a number of unrelated rows in one work, as Alban Berg or Arnold Schoenberg sometimes did, Barraqué starts by using one row, and then subtly alters it to get a second. This second row is then used for a while before being slightly altered again to make a third. This process continues throughout the work, so that the tone row at the end of the piece is completely different to that at the start.
Barraqué was in a car crash in 1964, and suffered bad health for the rest of his life. He died in Paris in 1973. His very small output has left him as a somewhat obscure figure, although his work is often praised, and the Sonata is seen as one of the great pianistic challenges of the 20th century.