Clayton Weatherston has had his application to appeal his murder conviction rejected.
The 35-year-old is serving a life sentence with a minimum non-parole period of 18 years for the 2008 murder of his former girlfriend Sophie Elliott.
Weatherston had sought leave in the Supreme Court to appeal the Court of Appeal's earlier dismissal of his appeal.
In its ruling today, the Supreme Court said two matters had been raised in the appeal.
The first was whether a television interview with a Law Commissioner during Weatherston's trial affected the fairness of the trial.