An Islamic State sympathiser who viciously mutilated and murdered his downtrodden young wife in front of their children in Melbourne has been sentenced to life imprisonment.

The man, who cannot be named to protect his children, attacked his 27-year-old wife with a knife at their Broadmeadows home in June 2016, gouging out her right eye and cutting off two of her fingers before she bled to death.

The remorseless 36-year-old must spend at least three decades in prison before being eligible for parole.

The man committed his "prolonged and vicious attack" in front of the couple's three young children, "who have obviously been traumatised by what they witnessed", Supreme Court of Victoria Justice Lex Lasry said on Thursday.

The man slashed at his wife's face, "the culmination of months, if not years, of physical violence", before her body was wrapped up in plastic and electrical tape.

The ice user then dumped the body in grassland near the Dallas tennis club, taking his children along for the ride.

One of his children previously said the man then waited on the boot of his car, to see "if mummy got up".

The man then took the children - aged two, four and six at the time - for pastries at a bakery, using their mother's bank card.

When the woman's body was found, she was unable to be identified due to her injuries, so DNA evidence was used.

The man was arrested in July 2016 when police attended his home to check on the welfare of the children, who were found bruised and injured.

Their home was in disarray with smashed windows and scribble and blood on the walls.

In sentencing, Justice Lasry said the killer, who has already spent 634 days in custody, showed no remorse.

He said he could not be satisfied the man's jihadist ideology led to the killing or that he was in a drug-induced psychosis at the time.

"I would not have thought your conduct in murdering your very compliant wife could be classified as an act of jihad," Justice Lasry said.

"What I am sure of is your conduct was grotesquely violent.

"The murder of your wife was the culmination of a long history of domestic violence."

The murder came after the woman had moved to Australia from Lebanon, pairing with the man in an arranged marriage, and was cut off from the support of her family and friends.

The man didn't allow the woman to speak freely, and controlled what she wore, refusing to send the children to school and wanting them to learn the Koran and about guns, swords, war and jihad.

The man had previously been treated with anti-psychotic medication, but his condition had stabilised before deteriorating in the first half of 2016.

The man also took a second wife, who was also subject to his violence, for a short time in 2011.