Szendi was ordained a priest on 24 December 1944. From 1969 until 1982, he was spiritual of the seminary of Esztergom. Szendi was appointed Apostolic Administrator of the Archdiocese of Veszprém as well as Titular bishop of Stephaniacum on 5 April 1982 and was consecrated bishop on 21 April 1982 by Laszlo Paskai. 