A man who stabbed his girlfriend to death because she would not cook him dinner fast enough has been sentenced to more than seven years' jail.

The Northern Territory Supreme Court heard that in August last year, Andrew Norman, from Yuendumu, had been drinking with his girlfriend for several days when they went to a Darwin home to prepare dinner.

Norman had chopped meat but when his girlfriend did not cook it as quickly as he wanted, he decided to poke her with a knife to speed up the process.

"I'll stab her a little bit, one time," he said to himself at the time.

But his lawyer told the court that in his drunken state the knife penetrated the woman's back.

The wound was 10 centimetres deep and severed an artery.

Norman tried to perform CPR and called an ambulance but the woman died.

Norman pleaded guilty to recklessly causing his girlfriend's death.

In sentencing, Justice Sally Thomas said it was an impulsive act that was out of character for the defendant but the fact he was affected by alcohol made the offence more serious.

Norman will be eligible for parole in 2012.