The decision by the High Court of Australia comes nearly a year after a unanimous jury found Cardinal George Pell guilty of molesting two 13-year-old choirboys in a Melbourne cathedral in the late 1990s, shortly after Pell became archbishop of Australia's second-largest city.
Pope Francis's former finance minister was sentenced to six years in prison in March.
He is no longer a member of Francis's Council of Cardinals or a Vatican official.
The Victoria state Court of Appeal rejected his appeal in August.
Pell, 78, is in a Melbourne prison. He did not attend the High Court in Canberra to hear the decision.
Two of the seven justices - Michelle Gordon and James Edelman - heard Pell's application for an appeal and unanimously approved it for a hearing by the full bench.
The court rejects around 90% of such applications.
An appeal hearing cannot happen before the judges return from their summer break in early February.
Pell's lawyers argued in their 12-page application for a High Court appeal that two state appeals court judges made an error in dismissing his appeal in August.
The judges made a mistake by requiring Pell to prove the abuse was impossible, rather than putting the onus of proof on prosecutors, the lawyers said.
They also said the two judges erred in finding the jury's guilty verdicts were reasonable.
Pell's lawyers argued there was reasonable doubt about whether opportunity existed for the crimes to have occurred.
Pell's lawyers also argued that changes in law over the years since the crimes were alleged have increased the difficulty in testing sexual assault allegations.
They say Pell should be acquitted of all charges for several reasons, including inconsistencies in the accuser's version of events.
Prosecutors argued there is no basis for the appeal and that the Victorian courts made no errors.
In their written submission to the High Court, prosecutors wrote that Pell's legal team was asking High Court judges to apply established principles to the facts of the case, which were already carefully and thoroughly explored by the state appeals court.
Pell was largely convicted on the testimony of one victim.
The second victim died of an accidental heroin overdose in 2014 when he was 31 without complaining that he had been abused.
After Pell lost his first appeal, the surviving victim said, "I just hope that it's all over now."
Pell must serve at least three years and eight months behind bars before he becomes eligible for parole.
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