Career
On 23 June 1973, he was ordained as a priest. On 17 March 1990, he was named auxiliary bishop of Olomouc and titular bishop of Tagaria. The principal consecrator at Graubner"s ordination as a bishop on 7 April 1990 was Olomouc"s then archbishop, František Vanák.
Vanák died on 14 September 1991, and on 28 September 1992, Graubner was appointed archbishop of Olomouc.
On learning of allegation of sexual abuse against Czechoslovakian priest František Merta, Graubner transferred the priest to another parish but did not report the matter to the police. A student of Palacký University of Olomouc Saints Cyril and Methodius Faculty of Theology subsequently laid criminal charges against both Merta and Graubner.