Hayden Brent McKenzie, 31, was sentenced to life imprisonment in the High Court at Wellington last month after earlier admitting murdering Jae Hyeon Kim in 2003.
It was his second life sentence, as he had already been convicted for his part in the murder of James John (Janis) Bambrough, a homosexual who was killed in 1999 at Westport.
McKenzie had served four years of that sentence when the 21-year non-parole sentence for the murder of Mr Kim was added.
Nelson police led the investigation into the murder of the economics student, who came to New Zealand to improve his English.
McKenzie's barrister, Greg King, confirmed an appeal against the length of the non-parole period had been filed in the Court of Appeal.
Sensible Sentencing Trust spokesman Garth McVicar said McKenzie should not appeal. If he lost, he should have his sentence extended.
He said, "Anybody who takes a life should spend the rest of their life behind bars, then the message might start getting through to these low-life crims.
"Our view is, if there is an appeal and it is lost, then the judge has the right and should be encouraged to extend the sentence because the appeal is a frivolous waste of taxpayers' money and the judge's time. Put another five years on for wasting time and money."
McKenzie was associated with a white supremacist group at the time of both killings.