A Northern Territory Supreme Court jury has taken less than three hours to deliver its verdict in the murder trial of a 28-year-old man from Arnhem Land.

The jury found Gavin Yunupingu not guilty of murder, which carries a mandatory life sentence in the territory.

Mr Yunupingu's father, Galarrwuy, the chair of the Northern Land Council and former Australian of the Year, was visibly relieved when the jury delivered the verdict but Gavin Yunupingu remained impassive.

Gavin Yunupingu kicked a woman in the head at his house at Ski Beach, near Nhulunbuy, in August 2000 and she died of a brain haemorrhage.

The court had heard she had been drinking heavily and had refused to leave his house.

The jury also found Yunupingu not guilty of manslaughter but guilty of committing a dangerous act causing death.

He has been remanded in custody for sentencing submissions next week.