Juraj Griglák was born to a family of musicians, his father played clarinet in the Czechoslovak Radio Symphony Orchestra and his mother sang in Slovak Folk Artistic Ensemble. He studied piano at a primary arts school and at the age of twelve he began playing drums and guitar. He studied double bass at the Bratislava Conservatory (1978–1984) and simultaneously played in funk groups Tamis and Tagore, The Bratislava Conservatory Big Band, Martin Kratochvíl & Jazz Q, Esprit band and Vlado Valovič’s VV System (performed on Copenhagen Jazz Festival 1987). Between 1987 and 1991, he furthered his studies of double bass at the Academy of Music and Performing Arts in Bratislava, and played with big bands of the Radio and Television.
He scored success as a member of the fusion music group, Stop Time (led by Matúš Jakabcic). The group performed at several Jazz festivals – Jazz in Duketown (Hertogenbosch, The Netherlands) and Jazz festival Aix en Provence (France). He has appeared repeatedly at the Bratislava Jazz Days. Many people still remember his jam session with Stanley Clark at BJD (1985). In the early nineties he played in ASH Band and The Quartet (CD Alice in Jazzland, 1992).
Juraj is a very successful studio musician having recorded more than 90 CDs. He appeared on the profile CD of Madre group (1994), he played in the Matúš Jakabčic Tentet (CD Matúš Jakabčic Tentet, featuring Greg Hopkins, 1998). In 2000, he recorded his first profile CD Bass Friends with special guest from New York, the excellent guitarist Ron Affif. The recording was highly evaluated by the well known and internationally acclaimed magazine Bass Player. The composition Codfish, a track from the CD, has been featured on the CD Sampler Station, released by another respected US magazine Bassics, as a recommended new release alongside such bass greats as Marcus Miller, Matt Garrison and Ray Brown. His second CD Time to Fly (2014) features special guests Poogie Bell and Patches Stewart. It won Esprit Prize as the best Slovak jazz CD (2015). In 2017 he released the CD Juraj Griglak & Company feat. Bobby Sparks, Poogie Bell, Chris Hemingway.
At present he is a leader of Juraj Griglak & Company, Pavel Morochovic trio, Miss Moravia and occasionally he collaborates with Ron Affif, Frank McComb, Iiro Rantala. He is a member of Poogie Bell Band and toured Europe with it several times (2012, 2013, 2016, 2017). He has led many jazz workshops at home and abroad. Juraj divides his time between jazz and classical music. In 1988, he toured Europe with the Gustav Mahler Youth Orchestra conducted by Claudio Abbado, Václav Neumann and James Judd.
Since 1991 he is a member of the Slovak Philharmonic Orchestra. Whith it he performed in most European countries, Japan, South Korea and the United States. In 1994, the Slovak Jazz Association awarded him the Ladislav Martoník Prize “Jazzman of the Year.”