A man described by a High Court judge in Northland as "dangerous and evil" has been denied permission to appeal against his conviction and 21-year minimum jail term for murder.

Wayne James Bracken was found guilty after a seven-week trial in the High Court at Whangarei of the murder of Jack Davis on February 25, 2011.

Bracken used a thistle grubber repeatedly until a fatal blow severed the carotid artery, causing Mr Davis to bleed to death.

Bracken was convicted of the kidnapping and murder of Mr Davis, as well as charges of aggravated robbery, assault with intent to injure and burglary.

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Bracken's co-accused in the death of Mr Davis, Neville Dangen, from Kaeo, was acquitted on all the charges. The jury took six hours to reach its verdict.

Within days of being sentenced to life imprisonment with a 21-year minimum non-parole period, Bracken appealed the conviction and sentence, but that was turned down by the Court of Appeal in March.

He then took a case to the Supreme Court asking for the right to appeal. In a decision released this week, the country's highest court dismissed his application for leave to appeal.

Supreme Court judges Justices Susan Glazebrook, Sir Terence Arnold and Mark O'Regan said in their decision it was not in the interests of justice to grant the application for leave to appeal.

During the trial, the jury heard how 30-year-old Mr Davis was kidnapped and "hog tied" before being driven into remote bush where he was murdered.

Justice Edwin Wylie said during sentencing: "It was calculated and vicious. It was, in effect, an execution."

The judge said Bracken was "dangerous and evil".