He enrolled in primary school in Davor, and Zagreb, eventually graduating in Slavonski Brod, after which he attended high school (Classical catholic gymnasium) for future priests on Šalata in Zagreb.

Škvorčević graduated from Zagreb Catholic Theological Faculty, where he also gained his master's degree, after which he went to Rome for additional specialization.

[2] Antun Škvorčević was ordered for a priest of the Archdiocese of Zagreb on 25 June 1972.

[2] on 3 May 1992, Pope John Paul II appointed him titular bishop of Editania and auxiliary bishop of the Roman Catholic Diocese of Đakovo-Srijem or Bosna.

On 5 July 1997, Pope John Paul II appointed him Bishop of, at the time, newly founded Diocese of Požega.