A teenager arrested in Victoria over his grandmother's murder in Sydney is accused of stabbing her to death in a frenzied attack using several knives.

Ethan Harwood, 19, faced Melbourne Magistrates Court on Friday as NSW police detectives applied to have him extradited to Sydney.

Harwood is accused of stabbing to death his 67-year-old grandmother Pauline Farrugia at her Penrith South home on Saturday.

Harwood had lived with grandmother for most of his life. She raised him until he went to live with his mother at Nhill in western Victoria about a year ago, according to a NSW police summary.

Police allege Harwood became drunk and upset at a barbecue at his sister's home on Saturday.

Other people overheard him telling his mother on the phone that he "wished he had never been born" and complaining of being physically abused by his grandmother when he was a child.

Police allege Harwood left the barbecue and went to his grandmother's house while in a "highly emotional state".

"Whilst inside the house, the accused attacked the deceased, inflicting at least 18 stab wounds to the torso of the deceased using several knives," police say.

"The attack appears to be uncontrolled and the accused broke several knives while attacking the deceased."

Officers found Ms Farrugia's body on Wednesday after one of her daughter's reported her missing.

Police allege Harwood tried to set fire to the house, which had been ransacked.

The stove and oven had been turned on, a smoke alarm was removed, and a woman's wallet had been set alight using matches.

The TV near where Ms Farrugia's body lay had also been switched on.

"Oddly, the television showing a DVD of the accused and the deceased on holidays in Hawaii in 2012," police noted.

Harwood was arrested at his mother's home on Thursday morning.

He is due to fly back to Sydney on Friday afternoon, and appear before Parramatta Local Court on Saturday.

AAP