Prosecutor Michele Williams, QC, told the Supreme Court the murder of Renea Lau, also known as Yuk Ling Lau, on June 28 last year, fell into the worst-case category of offending because of the brutality and duration of the attack and because of its random nature.

Scott Allen Miller has pleaded guilty to one charge of murder and two counts of rape after he chased Ms Lau over St Kilda Road and attacked her in parkland, after they crossed paths at 5.26am. Miller had been ejected from a bar and Ms Lau was on her way to work.

Ms Lau, 32, a Chinese national, had been at choir practice the previous night and was on her way to work at Ganache Chocolates in South Yarra when she encountered Miller and was so frightened she ran across St Kilda Road.

The court heard on Monday that prosecutors had, in written submissions, compared the attack to that on Jill Meagher, who was raped and then murdered by Adrian Bayley in Brunswick in September 2012. Bayley is serving life in prison, with a non-parole period of 35 years.

Ms Williams told the court Miller's offending comprised "crimes of the utmost gravity".

"It's a very serious example, we say, both of rape and of murder. The killing falls into the worst case of categories of murders ... because of the brutality of it, because of the sustained attack, the injuries that were inflicted on her and because this was a person who was simply going to work," she told Justice Betty King.

"A stranger murder with seemingly no apparent motive and once it's complete he walks away ... when one looks at the gravity of what he did, that's why in my submission it's one of the worst."

Justice King described the attack on Ms Lau as shocking, appalling and "every woman's nightmare", but said it could not be put in the same category as Bayley's offending given his record of convictions for violence and rape before he killed Ms Meagher.

The only criminal history Miller had previously, the court was told, was being charged with indecent exposure and theft in 1994 in Western Australia.

Miller was treated in hospital for drug and alcohol abuse around that time, the court heard, and medical reports showed he did not have any mental health problems.

Miller was homeless and sleeping rough in the weeks before the murder, and in the lead-up had spent more than seven hours in two city bars, where he had consumed alcohol, harassed several women and offended several other patrons.

Ms Williams said patrons in Transport Public Bar, in Federation Square, and The Carlton, in Bourke Street, had described him as rude and obnoxious, although he did not appear overly affected by alcohol and did not appear affected by drugs.

He was ejected by security staff from The Carlton at 5.07am, the court heard, and walked through Melbourne's central business district and along St Kilda Road, where he encountered Ms Lau, who was walking toward Flinders Street station to catch a train to South Yarra.

Ms Williams said it was not known what was said when the pair interacted.

"We don't know what was said. Whatever it was frightened Renea into running across St Kilda Road," she said.

The prosecutor said Miller chased Ms Lau and they struggled on a median strip, before he dragged the woman into the gardens and savagely beat her, near the Police Memorial.

Ms Lau was repeatedly punched to the face, had her head smashed on concrete and force was applied to her neck. Miller then twice raped her and left Ms Lau's body at the scene, with clothing on top of her.

Walkers discovered her body.

Afterwards, the court was told, Miller walked to Kooyong train station and caught a train to Glen Waverley, where he bought some shoes - he left his in the gardens, along with a bank card - and tobacco and then hitched a ride to Gippsland.

Two women gave Miller a lift but left him in Orbost after feeling uncomfortable in his company, while another woman gave him a lift over the Victoria-NSW border. He was arrested in Eden two days after the attack on Ms Lau.

In an interview with police, Miller said he was "blind drunk" when he attacked Ms Lau, but could not remember how many times he struck her.

"I attacked a girl and didn't intend to kill her and, um, raped her. Um, I wasn't aware that she died from the incident and the whole thing was I just exploded," he told detectives.

Miller told police he heard God tell him he would be charged and that he was ashamed of himself, but was comfortable with being jailed.

"I am happy that I won't now be living on the streets and I'll be in jail and I'll have food and stuff like that," he said.

Ms Williams said Miller was with Lau for about 80 minutes after first interacting with her, as an electrician had walked past the pair at 6.45am while on his way to work and tried to look away, as he thought they were a couple having sex.

A group of Ms Lau's family members were in court, and victim impact statements from her parents, boyfriend and siblings were tendered to court, but not read aloud.

Relatives have told police she was a popular, much-loved woman who had settled in Melbourne after travelling in Australia, and was planning to return to Hong Kong to visit family.

Defence counsel Stephen Payne said Miller had conceded his crime was a "random act of terrible violence", and had made no attempt to justify or play down his offending.

The hearing was soon after adjourned when Mr Payne became unwell. Victoria Legal Aid is expected to brief another barrister to replace Mr Payne for when the case returns to court.