Jonni Hansen, who leads the Danish National-Socialist Movement from Greve, near Copenhagen, claims to have the 12 pupils needed to start the school. He says they are the children of acquaintances.
The school can be approved and subsidised by the ministry of education if certain financial and legal requirements are met and if education is of suitable quality.
"The private independent schools Act is very broad," says Henrik Kober, a head of division at the ministry of education. "One can start a private independent school on any chosen ideological basis."
The ministry will assess the school's purpose, including potential breaches of the law on racism. "But breach of a law is not in itself sufficient to deny a school a subsidy," says Henrik Kober.
Neither the Social Democrat-Social Liberal coalition government nor the Socialist People's party is prepared to change the law. Anyone should be able to start a private independent school as long as they follow the rules, they say.
But Brian Mikkelsen, education spokesman of the Conservative People's party, says, "We must consider whether our liberalism has gone too far. I am ready to propose a special law that will require private independent schools to operate on a democratic basis."
* Denmark's liberal freedom of expression and freedom of assembly laws have turned the country into a notorious international distribution centre for Nazi propaganda.
A polemical book on immigrants and refugees in Denmark for 13 to 16-year-olds has caused so much controversy that it was temporarily withdrawn by the educational publishing arm of Gyldendal, Denmark's largest publisher.
Now available again with a single correction, Kare Bluitgen's Nye Danskere (New Danes) includes racist jokes and claims that immigrants "cannot read and write and have no knowledge of democracy, charity and tolerance".
New Danes has been condemned by the Islamic-Christian Study Centre and the Bishop of Aarhus, Kjeld Holm, who chairs the Danish board of ethnic equality. The study centre says the book depicts ethnic minorities as "cheats, sexual deviants, egoists and criminals".
"This isn't about censorship and freedom of expression but morals and ethics," says Kjeld Holm. "It's a poor book and, because it will be used in schools, it should be rewritten. We must treat immigrants and refugees properly."
Mr Bluitgen, a trained teacher who describes himself as "generally anti-racist and in favour of integrating refugees", does not understand the criticism.
"Some of the jokes are horrible, " he admits, "but they already exist at schools. If we don't raise the subject it will just get worse."