Steve Constantinou, 49, was jailed for 24 years with a non-parole period of 20 after a Supreme Court jury found him guilty of murdering the 65-year-old grandmother on October 11, 2011.

He applied for leave to appeal his conviction, claiming it was a miscarriage of justice, but the Court of Appeal on Monday rejected the application.

Constantinou claimed Ms Martin had died during a sex game gone wrong.

Justice David Ashley said Constantinou had substantial debts when he murdered Ms Martin and pawned her jewellery.

After his arrest, he had provided different versions of what had happened.

"He told the police that that the deceased was distressed and had strangled herself in the bathroom," Justice Ashley said in his judgment.

"He had panicked and decided to get rid of the evidence by disposing of her body and her jewellery."

Justice Ashley said during the trail, the Crown case had demonstrated that O'Martin had given $8500 to Constantinou.

"It hypothesised that she wanted the money repaid and to avoid repayment in circumstances where his financial position was parlous, the applicant strangled her with murderous intent.

"Having killed her, the Crown argued, he took her jewellery, sold it to a pawnbroker, and then disposed of the body before going to a hotel, having a winning bet and later going to another hotel where he collected on his winning bet."

The judge said Constantinou's defence during his trial was that he caused Ms Martin's death "by compression of her neck ... in the course of a sexual episode involving erotic asphyxiation which had gone wrong".

Justice Ashley said the Crown had contended that Constantinou's behaviour after the crime was not the conduct of a man in a panic over a sex game that had gone terribly wrong.

He said a forensic pathologist gave unchallenged evidence that it was impossible for Ms Martin to have strangled herself, and there was a considerable body of circumstantial evidence that strongly pointed to Constantinou having murdered the deceased.

Constantinou told the jury Ms Martin had introduced him to bondage and he had never heard of the term 'erotic asphyxiation' until after his arrest.

He claimed not to have known about her involvement in the sex industry until after her death.

Constantinou had met Ms Martin, Melbourne's most famous stripper and prostitute, early in 2011 at the South Melbourne Market and they became friends. Her husband, Arthur, had died on Father's Day, 2010.

Ms Martin was well known in the industry for her extreme acts, and sometimes had sex on stage during her shows.

She had accumulated about $3 million in assets during her career, including several properties and luxury cars. Her friends said she would never get involved in bondage because she always had to be in control.