A convicted killer who stabbed a woman to death in 1986 has pleaded guilty to the murder of Melbourne woman Sarah Cafferkey.

Ms Cafferkey was stabbed multiple times at a house in Bacchus Marsh on November 10 last year.

Her body was later found in a wheelie bin at a Point Cook home.

Steven Hunter, 47, appeared briefly in the Melbourne Magistrates Court today, wearing his green prison tracksuit.

Ms Cafferkey's mother was in court to hear Hunter admit murdering her daughter.

He will face the Supreme Court next month.

Hunter served 13 years in jail for the stabbing murder of 18-year-old Jacqueline Mathews in 1986.

Ms Mathews, a supermarket workmate of Hunter's, was stabbed seven times in a car park in Tullamarine.

Hunter claimed Ms Mathews had abducted him in her car and brought him to the car park in order to make a sexual advance, a story the sentencing judge rejected.

The judge ruled Hunter had stabbed Mathews after she rejected his advances.

Hunter had completed his parole on other matters just days before he killed Ms Cafferkey.

Murder investigation

Ms Cafferkey left her Bacchus Marsh home on November 9 and was seen at a friend's house nearby the next day.

Her abandoned car was found on Owen Street in Maribyrnong several days later.

On November 19, police swooped on a home in Point Cook, west of Melbourne, and found Ms Cafferkey's body in a wheelie bin.

It is believed Hunter was living at or staying at the home at the time of the murder.

Hunter was arrested in dramatic circumstances in a raid on a flat at Hawthorn a week later.

Hunter had exchanged Facebook messages with Ms Cafferkey in the days before her disappearance.