A former Australian archbishop sentenced for concealing child abuse had his conviction quashed after winning his appeal.

Philip Wilson had been charged with concealing crimes by late paedophile priest Jim Fletcher in the Hunter region of New South Wales in the 1970s.

The 68-year-old was sentenced to 12 months' imprisonment last May and had spent four months in home detention at his sister's house.

He was one of the highest-ranking church officials convicted of covering up child abuse.

"There is no proper basis upon which I can rely to reject the evidence of the appellant," Judge Roy Ellis said before he handed down the ruling.

The judge noted "inconsistencies" with the accuser's statements regarding an alleged conversation he had with Mr Wilson about the abuse.

"This court could not be satisfied beyond reasonable doubt that the conversation took place at all," Judge Ellis said.

Mr Wilson resigned as Archbishop of Adelaide in July after then prime minister Malcolm Turnbull called on the Vatican to sack him.

There was no dispute during the initial trial that Fletcher, who died in custody in 2006, sexually abused an altar boy, with the hearing focused on whether Mr Wilson, then a junior priest, knew about it.

He has long denied the charges and initially resisted calls to quit.

Mr Wilson served as a priest in New South Wales before Pope John Paul II appointed him Bishop of Wollongong in 1996. Five years later, he became the Archbishop of Adelaide.

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Prime Minister Scott Morrison in October made an apology on behalf of Australia for failing to protect thousands of survivors of institutional child abuse.

He was responding to a five-year royal commission, ordered by the government after a decade of pressure to investigate widespread allegations across the country.

The commission was contacted by more than 15,000 survivors who detailed harrowing allegations of abuse involving churches, orphanages, sporting clubs, youth groups and schools, often dating back decades.

Australian Catholic leaders vowed in October that the church's "shameful" history of child abuse and cover-ups would never be repeated.