He was one of the cardinal electors who participated in the 2005 papal conclave that elected Pope Benedict XVI.
He was ordained a priest at the age of 23, on 3 March 1951, joining the Order of Friars Minor.
After his ordaination he did pastoral ministry in the diocese of Nagyvarad before being sent to Budapest for further studies. In Szeged, he served as episcopal master of ceremonies from 1952 to 1955.
After this he was a faculty member and librarian of its seminary, 1955–1962.
Thereafter serving as prefect of the Interdiocesan Seminary, faculty member and spiritual director until 1965. He later served as a faculty member and spiritual director and finally rector of the Central Seminary, Budapest. On 2 March 1978 he was chosen Apostolic Administrator of Veszprém, becoming a bishop that same day, with the titular see of Bavagaliana.
Pope John Paul II appointed him Archbishop of Veszprém on 31 March 1979.
He was appointed Primate of Hungary and Archbishop of Esztergom on 3 March 1987.
He was created Cardinal-Priest of Santa Teresa al Corso d’Italia. In 1993 the dioceses of Esztergom was united with that of Budapest, so that Cardinal Paskai was the first Archbishop of Esztergom-Budapest.
Cardinal Paskai retired as Archbishop of Esztergom-Budapest in 2002.