The High Court has refused to hear an appeal by a Northern Territory Aboriginal man convicted of unlawful sex with his 15-year-old promised wife.

Justices Gummow, Hayne and Heydon have dismissed an application by Jackie Pascoe Jamilmira for leave to appeal against a sentence by the Territory Court of Appeal, following his conviction in 2002.

Jamilmira from Maningrida was initially sentenced to 13 months jail with a four-month non-parole period but he appealed to the Supreme Court, arguing he had acted within his rights under customary law.

The court reduced his sentence to 24 hours but the Director of Public Prosecutions took the case to the Court of Appeal, which increased the sentence to a year, suspended after a month.