Leoš Čepický graduated from the East-Bohemian Conservatoire in Pardubice in 1985 under Professor Ivan Štraus. At the Prague Academy of Performing Arts, he studied violin with Jiří Novák and Chamber Music with Antonín Kohout - both of these musicians were members of the world-renowned Smetana Quartet.
He started his promising career in his early teens, when he won the first prize and Laureate title at the Jaroslav Kocian International Violin Competition. Other prizes followed at the Gorizia Competition and the Václav Hummel Competition in Zagreb. In 1994 he was the outright winner of the Ludwig van Beethoven International Violin Competition in Hradec nad Moravicí. Since that time, he has given many recitals as well as solo concerto performances with various orchestras. In J.S.Bach´s 250th Jubilee Year in 2000, he performed in concert Bach's complete Sonatas and Partitas for solo violin and two years later he released the whole cycle on CD.
In 1985 the Wihan Quartet was formed at the Prague Academy of Performing Arts. In 1988 the Quartet won the first prize at the prestigious Prague Spring Competition and three years later they won the London International String Quartet Competition, whose chairman was Yehudi Menuhin. After this success, the door to the whole world, from the USA to New Zealand, was wide open to the Wihan. During their career, they have released over 40 CDs, including the complete set of Beethoven´s 16 Quartets, which were recorded live for the British label Nimbus Alliance between October 2008 and March 2009. Another unique CD, a recording of Paganini´s 24 Caprices, arranged for string quartet by William Zinn, was released in 2009 on the same label.
Leoš Čepický was appointed Head of Strings at the Prague Academy of Performing Arts in 2010, having taught violin there for several years.

Since 2017 Leoš Čepický is a concertmaster of Prague Chamber Orchestra.
He plays on a copy of Guarneri del Gesu 1741' 'Vieuxtemps', made in 1990 by Jan Baptista Spidlen.