China applied for his extradition in May last year, but because there is no extradition treaty between New Zealand and China, the request had to be dealt with by then-Justice Minister Simon Power, who allowed the case to go to court.
Several dates for an extradition hearing have been set, but Kim has requested they be adjourned while his lawyers seek his release from custody.
Numerous applications for bail have been declined.
Last month, Kim applied to the High Court for a writ of habeas corpus - a claim of being unlawfully detained in custody - but Justice Stephen Kos dismissed the application.
His lawyers then sought to overturn the ruling in the Court of Appeal, claiming there was no power under the Extradition Act to hold Kim in custody.
They also claimed there was no evidence Kim could be extradited under the Act because he had not been convicted or accused of an offence and was wanted only for questioning.
The Court of Appeal disagreed, and agreed with Justice Kos that there was power to hold Kim in custody and that he could be extradited under the Act.
The case is far from over, however, with the court noting that Kim's defence team is drafting a statement of claim for a judicial review of the case - potentially further delaying an extradition hearing before a District Court judge.
If Kim is found to be eligible for extradition it will still be up to Justice Minister Judith Collins to decide whether to surrender him to Chinese authorities.
Ms Collins could decide not to extradite Kim if there are grounds to believe he is in danger of being tortured or sentenced to death.
Chinese authorities have said they would not seek a death penalty if Kim was extradited.
Human rights groups have criticised of the use of the death penalty in China, which executes more people a year than any other country where capital punishment is legal.
