Convicted double killer and white supremacist Hayden McKenzie has had his appeal against his 21-year non-parole sentence turned down.

McKenzie, 31, admitted killing Korean backpacker Jae Hyeon Kim near Westport in 2003 and was last year sentenced to life imprisonment.

He was already four years into a life sentence for his part in the murder of James John (Janis) Bambrough, a homosexual killed at Westport in 1999.

At the appeal hearing on April 30, McKenzie's lawyer Greg King told the Court of Appeal the second life sentence was "manifestly excessive" as 21 years on top of the four years already served equated to a non-parole period of 25 years.

The "proper" non-parole period should have been 17 years, he said.

The Court of Appeal judgment, released yesterday, dismissed McKenzie's appeal, saying it was not appropriate to encompass the four years he had already spent in custody as part of the sentence.

"Each of these killings was callous, wanton and despicable. The total effective sentence was no more than was needed to reflect the total culpability."