Cardinal George Pell, 77, wore a black suit and black shirt with a cleric's collar when he appeared for the Victoria state Court of Appeal hearing before three judges.
He came and went from the court as the sole occupant of a prison van, and said nothing during the hearing.
Pell's lawyer Bret Walker argued for more than five hours that the five verdicts against Pell were "unsafe and unsatisfactory" and should be overturned.
The lawyers cited former High Court Justice Michael McHugh, who said "juries are likely to be affected by the prejudices and even the hysterias that from time to time are found in the community".
The prosecution will argue on Thursday why the verdicts were sound and should stand. Whoever wins, the case could reach the High Court, Australia's ultimate arbiter.
A jury unanimously convicted Pell in December of orally raping a 13-year-old choirboy and indecently dealing with the boy and his 13-year-old friend in Melbourne's
St Patrick's Cathedral in the late 1990s. Pell had become archbishop of Melbourne only months before.
Court orders had for months prevented publication of the details of that trial and an earlier trial on similar charges that had ended in September with a deadlocked jury.
Pell was sentenced in March to six years in prison, and is held in special protective custody.
While Pell remains Australia's highest-ranking Catholic, the Vatican is conducting its own investigation into the convictions of Pope Francis's former finance minister.
Francis's papacy has been thrown into turmoil by clerical sexual abuse and the church's handling of such cases worldwide.
In a little more than a year, the Pope has admitted he made "grave errors" in Chile's worst case of cover-up, Pell was convicted of abuse, a French cardinal was convicted of failing to report a paedophile, and a third cardinal, former US church leader Theodore McCarrick, was defrocked after a Vatican investigation determined he abused children and adults.
Mr Walker told the three judges the main ground for appeal was that the jury could not have found Pell guilty beyond reasonable doubt on the evidence.
In written submissions, Pell's lawyers said more than 20 prosecution witnesses who had an official role in the Sunday mass in 1996 gave evidence that the offences did not or could not have occurred.
"This evidence constituted a catalogue of at least 13 solid obstacles in the path of a conviction," the lawyers said.
"No matter what view was taken of the complainant as a witness, it was simply not open to a jury to accept his words beyond reasonable doubt," they added.
Pell's lawyers argue in their submissions that the "the evidence showed the offending was impossible".
Demonstrator Joe Mitchell, 83, drove more than 600 miles from his home in Newcastle, New South Wales, to Melbourne to protest outside the court against the church response to child abuse.
"I'm a victim. I hope they put a rope around his ... neck," a tearful Mr Mitchell said. "They say 'how could you remember back 70 years?' I remember everything."
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