A Melbourne man who brutally murdered and mutilated his wife in front of their three young children has been sentenced to life in prison.

Police believe the 36-year-old Broadmeadows man, who cannot be named, may have killed his wife because she didn't want him to join the Islamic State (IS) group in Syria.

The man will be eligible for parole in 30 years.

In July 2016, the three children told police they had witnessed their father "slaughtering" their 27-year-old mother with a knife in the lounge room of their house.

One of the children told detectives his mother's "body was nothing but blood".

The children told police their father wrapped the woman's body in electrical tape, plastic and a doona before putting it in the boot of the family car.

It was alleged he then put the children in the car and drove to grassland next to tennis courts at Dallas, in Melbourne's north, where he dumped the body before taking his children to a bakery to buy pastries.

The court heard the woman had knife wounds and showed evidence of blunt force trauma, and that she most likely bled to death.

Her body, which was found by a member of the public, took weeks to identify.

A 'violent and horrific' crime

Police alleged the man had previously told his brother-in-law he had fought with his wife over his desire to go to Syria to join IS, and had sliced her hand with a knife six months before her death.

However, Supreme Court Justice Les Lasry on Thursday said he did not accept Islamic extremism was the sole reason for the killing.

He said the man's crime was "grotesquely violent … and horrific".

"The very thought of a child being able to describe their father slaughtering their mother is beyond belief," Justice Lasry said.

He said the man's brutal actions had an impact on his children "which will continue for the rest of their life".

The court had previously heard the man had extremist Islamic beliefs and used the drug ice.

During the sentencing, one man in the public gallery was removed from the court for gesturing to the offender.

Man was weird, paranoid: second wife

During his committal hearing, the court heard the man believed his second wife, whom he married under Islamic law while still legally married to the woman he killed, was an ASIO spy.

The second wife, who divorced the man after six weeks in 2011, told the hearing her former husband's behaviour during their polygamous relationship was weird and paranoid.

The man cannot be identified under a court order to protect the identity of the couple's children.