On 12 April 1942 he was ordained priest. After having served in the military, he served as chaplain. From 1946 until 1952 he was prefect of studies at the minor seminary in Hollabrunn. He obtained a doctorate in theology in 1949 and from 1952 until 1974 he was a professor in religion.
During this period, he was involved in promoting pilgrimages to the Sanctuary of Our Lady of Roggendorf and on 13 October 1969 he organized his first monthly pilgrimage. He then became rector of the sanctuary, and served as organizational director of pilgrimages. In 1970 he became spiritual director of the Legio Mariae in Austria.
In 1974 he joined the order of St. Benedict and made his solemn profession on 8 September 1980.
On 15 July 1986 he was elected Archbishop of Vienna. In the same year he was nominated Ordinary for the faithful of the Byzantine rite residing in Austria. He has also served as president of the Austrian Bishops Conference.
Created and proclaimed Cardinal by John Paul II in the consistory of 28 June 1988, of the Title of Sts. Joachim and Anne al Tuscolano.
Archbishop emeritus of Vienna, 14 September 1995.
Cardinal Hans Hermann Groër died on 24 March 2003.