Beckham then went to the Supreme Court and alleged an abuse of process by police relating to the granting of three interception warrants obtained for electronic surveillance.
He was arrested after a six-month inquiry in 2008 during which police tapped his cellphone and bugged his car.
Police listened to privileged conversations between Beckham and his lawyer while the former was in custody 18 months before his trial in the High Court.
The Court of Appeal had ruled there was no abuse of process by police and the interception warrants were properly issued.
The Supreme Court granted him leave to appeal in July 2013 and the approved ground of appeal is whether he should have received a reduction in his sentence for breach of his rights under the New Zealand Bill of Rights Act 1990.
During his Auckland trial, it was revealed Beckham was the kingpin of a methamphetamine syndicate.
Detectives found $865,720 hidden in a vehicle at his home when Beckham was arrested in 2008. Beckham's assets and cash worth more than $10 million have been restrained.
Beckham previously co-owned the ITM store in Mangonui, ran a property development company, hand-planted a large olive orchard and once owned a large commercial fishing fleet.
The Supreme Court will hear his appeal in Wellington on February 10-11.