Jaromír Podešva was born into the family of a Brno violin-maker, Jan Podešva, where from a tender age he came into contact with art music at family music-making sessions (in those days he already played the piano, violin and viola). As a child, too, he began to compose spontaneously pieces that had their roots in the Czech Dvořák-Novák-Suk tradition. Having passed his School-Leaving Examination at the grammar school in Brno Židenice in 1948, he took a one-year follow-up course at the Brno Conservatoire (1946-1947), then he studied composition with Jaroslav Kvapil at the Janáček Academy of Arts (1947-51), and under the guidance of the same teacher continued with a three-year postgraduate course at the Brno Academy. After his studies Podešva was secretary of the Union of Czechoslovak Composers in Prague (1956-59), and later was chairman of its branch in Brno. Since 1969 he had been teaching composition and music theory at the Conservatoire in Ostrava (until 1990).

A significant impact was made on Podešva' s compositional style when he spent almost one year in west Eurogean countries and the United States (1960-61), where he became familiar with the works of Stockhausen, Boulez and Honegger and studied with Dutilleux and Copland (on a scholarship from UNESCO). Based on his experience abroad he published an account of his musical travels in a book entitled Contemporary Music in the West (publ. Panton 1963). His Symphony No. 2 for Strings and Flute constitutes a turning point in his style, whose characteristics are a synthesis of the principles of extended tonality and dodecaphony. Most of the compositions of this period are named after a literary work that captured the composer's imagination, as for example his Symphony No. 3, whose music forms a parallel to actual texts, or his Symphony No. 6 and Clarinet Quintet, where there is a mere indication of an extra-music subject. He drew some general conclusions from his own practice as a composer in his theoretical treatises: ‚The Possibilities of Cadences in the Twelve-Tone System‘ (publ. by Panton 1974) and ‚Introduction to the Study of Composition‘ (MS).