The 78-year-old former adviser to the Pope is currently serving a maximum six-year prison sentence for the sexual abuse of two former choirboys at St. Patrick's Cathedral while he was the Catholic Archbishop of Melbourne in the 1990s.
Pell has to serve three years and eight months in jail before being eligible for parole, ABC News Australia reported.
The former Vatican treasurer is the most senior Catholic cleric to be convicted of such crimes, but he has consistently maintained his innocence.
After losing an earlier appeal, Pell now hopes his case will be heard by Australia's top court. The high court on Tuesday confirmed it had received the application through its Melbourne registry. However, there is no guarantee that the court will agree to review it.
Last December, a jury unanimously convicted Pell of sexually abusing the 13-year-old boys inside St. Patrick's Cathedral. The convictions included one count of sexual penetration and four counts of committing indecent acts.
The verdict was kept secret from the public until February, when additional charges of sexual offences against Pell were withdrawn by prosecutors.
In his failed first appeal, Pell had asserted that the guilty verdict had relied unreasonably on the testimony of one victim. His second victim died of a drug overdose in 2014.
Pell's conviction rocked the Catholic Church following which he was demoted from the Pope's inner circle last year, but the Vatican continues to face calls for Pell to be defrocked.
Pell will be eligible for parole in October 2022.
( With inputs from IANS )