West Australian mass murderer Anthony Robert Harvey has abandoned his attempt to ever be released from jail for killing five members of his family, including his three daughters aged under three, in their home.

Key points: Anthony Harvey murdered his family in his suburban Perth house

Anthony Harvey murdered his family in his suburban Perth house The judge who sentenced him said his crimes were "exceedingly brutal"

The judge who sentenced him said his crimes were "exceedingly brutal" He'll have to make a special application if he wants to lodge a future appeal

WARNING: This story contains graphic content that some readers may find upsetting

Harvey was 25 years old when he became the first person in WA ever to be jailed with no possibility of release.

The sentence came after he pleaded guilty to murdering his 41-year-old wife Mara, their three-year-old daughter Charlotte and two-year-old twins Alice and Beatrix, and their grandmother, 73-year-old Beverley Quinn.

He killed them all at the family's home in the Perth suburb of Bedford in September 2018, with his Supreme Court sentencing hearing told he had planned the murders for days and written in a journal about eliminating his family.

Justice Stephen Hall sentenced him to life in prison, ruing it was "necessary to make an order that [Harvey] never be released in order to meet the community's interest in punishment and deterrence".

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 3 minutes 13 seconds 3 m 13 s Anthony Harvey is sentenced to never be released from jail

Justice Hall said he struggled to find the words that were adequate to convey the magnitude of what Harvey had done, describing his crimes as "exceedingly brutal".

Daughters died as they slept

The court heard the then-24 year-old attacked his wife first as she arrived home from her night job.

He then targeted his daughters while they were sleeping.

Harvey's wife Mara was his first victim before he turned his attention to their daughters. ( Facebook: Mara Quinn )

The next morning, Mara's mother Beverley Quinn arrived, as she usually did, to help look after the children, and Harvey set upon her.

He stayed with the bodies for days, covering his victims with doonas and bunches of flowers and writing letters apologising for what he had done.

He then drove to the Pilbara town of Pannawonica, where he confessed to his father who called the police.

Harvey was immediately taken into custody and has been there ever since.

Two weeks after the sentence was imposed, and seven days before the cut-off point, Harvey lodged an appeal which said he would argue the order that he never be released "was unreasonable, having regard to the circumstances of the offence and the personal circumstances of the appellant".

He said he was not legally represented but would be applying for funding through legal aid.

WA's only 'never to be released' sentence

The appeal notice appeared to have been personally signed by Harvey and said his address was Hakea Prison in Canning Vale.

He has now withdrawn his appeal notice, meaning the historic ruling will not be tested by WA's highest court.

If he ever does change his mind, he will have to make a special application to convince the Appeal Court that his case should be heard "out of time".

Police found Harvey's victims at the house a week after they were murdered. ( AAP: Richard Wainwright )

No other person in WA has ever received a "never to be released" sentence, a provision that was introduced under changes to the state's homicide laws introduced in 2008 by the then-Labor government.

Before that, the only person who faced the possibility of never being released was William Patrick Mitchell, who murdered four members of one family with an axe in the Mid West town of Greenough in 1993.

At one point there was an order that Mitchell should never be granted parole, but it was overturned on appeal.

William Patrick Mitchell killed four people from one family with an axe in Greenough in 1993. ( ABC News )

He was then given a life term with a 20-year minimum, which expired in 2013.

Mitchell applied for release on parole but was refused.

Under the legislation, offenders are eligible to be considered for parole every three years after they have completed their term.

Every one of Mitchell's applications has been refused.