"The application for leave to appeal against the conviction is dismissed," said Judge Joop Labuschagne in the High Court in Johannesburg.
It was a "desperate attempt by the applicant not to reveal the truth", he said.
"I cannot find that there is a possibility that another court will come to a different conclusion."
Moodley's supposed "true
story" of the events surrounding the crime was barely believable, Labuschagne said.
"The applicant's 'true story' is riddled with
improbabilities."
He said Moodley's statement that he had been offered R1
million by three men to help them kidnap another man was also
questionable.
"It is in my view ridiculous," said Labuschagne.
Moodley was found guilty in 2005 of the murder and kidnapping of Matthews, 21, and of extorting money from her father.
He was sentenced to life imprisonment for the murder, 15 years for the kidnapping, and 10 years for the extortion.
Labuschagne said he needed to take into account the
delay in approaching the court. An application to appeal was meant to be
made within 14 days.
"In my view he has failed to properly explain why it took him nearly six years."
The fact that Moodley had admitted to committing the
crime was further ammunition against considering the appeal, the judge
indicated.
"The applicant repeatedly confirmed his guilt for a number of years."