In 1961, he moved with his parents Tomislav and Vesna to Sesvetski Kraljevec near Zagreb. His father was from Sesvetski Kraljevec and he too was a singer. His mother was a tailor.
In Zagreb, Stublić studied philosophy, but he never graduated. During the ex-Yugoslav New Wave, he was also known as Jura Jupiter. He started his musical career as a member of Croatian rock group Azra in 1977. The following year, after a few arguments with the frontman of Azra, Branimir "Johnny" Štulić, he left the band along with Mladen Juričić Max and Marino Pelaić Barracuda to form his own band Film. He pens most Film songs and he is one of the most popular songwriters in Croatia. Many still remember the war-related song "E, moj druže beogradski" (Oh, my Belgrade comrade).
In 1993, he took a break from Croatian music scene, but returned in 2000. He is still active.