Pospišil was born on 9 June 1904 in Vukovina, Austria-Hungary (modern-day Croatia) to Ladislav and Marija Kralj and was educated as a mechanic.

[1][2] On 22 March 1929, Pospišil, Mijo Babić, Marko Hranilović, and Matija Soldin murdered Toni Šlegel, the chief editor of newspaper Novosti from Zagreb and president of Jugoštampa, which was the beginning of the terrorist actions of Ustaše.

Stjepan Javor, the leader of the Croatian Rights Youth, the nationalist organization in which the assassins were members was sentenced to 20 years in prison.

Ustaše retreated toward Gacko and Avtovac and burned the village of Zborna Gomila, after four died on the battlefield including Zvonimir Pospišil.

[5][6][7][8] During the uprising in eastern Herzegovina the other two conspirators of the assassination of King Alexander, Mijo Babić and Antun Pogorelac, were also killed during their attacks on rebels.