The High Court of Australia will next month hear an application by Corey James Martin for leave to appeal the 22½ year jail sentence he received for the murder of Andre Le Dinh.

The case is the final legal avenue for Martin, who has already unsuccessfully appealed the verdict and the sentence to the ACT Court of Appeal.

In August, both bids were dismissed.

Martin, who is also known as Budgie, has appealed to the High Court for leave to appeal against that decision.

Mr Le Dinh, 26, died of head injuries after the 110 kilograms, 189 centimetres Martin bashed him during a drug robbery at the victim's Belconnen unit on May 2010.

Martin knocked on the door, beat the diminutive 48 kilograms, 165cm victim unconscious, stole 1.8kgs of cannabis and $30,000 cash, and left Mr Le Dinh with skull fractures and choking on his own blood.

Martin admitted he had been to the unit and the pair had fought about drugs, but claimed Mr Le Dinh had been standing and conscious when he left the unit.

In 2013, an ACT Supreme Court jury found him guilty of the murder on the basis that, although he did not to kill Mr Le Dinh, he had intended to cause the victim serious harm.

Justice John Nield sentenced Martin to 22½ years' jail, with a non-parole period of 17½ years.

Martin's legal team unsuccessfully appealed the verdict and sentence, arguing the judge had made a number of errors during the trial, that the sentence did not fit in with past murder sentences, and that the parole period had been wrongly set.

The Court of Appeal dismissed the appeal in August, finding all 12 grounds of appeal had failed.

Martin has now sought special leave to challenge that decision in the High Court.

Documents, filed in the High Court, argued the appeal court had "erred in holding that … the appeal against sentence were directed to issues of weight in the exercise of the sentencing discretion rather than impugning specific error in the process".

"In failing to examine this as a process error rather than a weight complaint, the Court of Appeal improperly constrained itself in the review of the applicant's sentence.

"It is in the interests of the administration of justice that the applicant not be refused proper appellate review of his sentence."

Martin's lawyers asked the court to allow the appeal and the matter be sent back to the Court of Appeal, constituted of different judges, to be determined by law.

But the ACT Office of Public Prosecutions has opposed the application for leave to appeal.

In his response to the application, ACT Director of Public Prosecutions, Jon White, SC, argued Martin had not demonstrated an error and had sought to "confect a new species of specific error" which distracted from established case law.

"The interests of the administration of justice in the particular case do not favour the grant of special leave," he wrote.