Archbishop of Adelaide Philip Wilson was found guilty on Tuesday following a magistrate-only trial at Newcastle Local Court near Sydney.
The 67-year-old, who denied knowing a paedophile priest had sexually abused two altar boys in the 1970s, faces up to two years in prison.
Both former altar boys claimed they told Wilson in 1976 of abuse they had suffered at the hands of James Fletcher.
Found guilty in 2004 of nine counts of child sex abuse, Fletcher died in prison in 2006 after suffering a stroke. He had been serving a nearly eight-year sentence.
One of the former altar boys told the court in December 2017 that he described to Wilson in graphic detail the abuse he experienced.
Wilson said such a conversation slipping his mind would have been unlikely, telling the magistrate: "I don't think I would have forgotten that."
The Catholic leader also said that taking prescribed medication had helped treat the early stages of his Alzheimer's disease and improve his memory, "although it's not perfect".
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