James Gargasoulas, who went on a rampage through Melbourne's Bourke Street and mowed down pedestrians, has been found guilty of murdering six people and endangering the life of 27 others.

A Supreme Court jury took just over an hour to find the 28-year-old, who admitted killing six people in a Bourke Street rampage on January 20 last year, guilty of all charges.

Despite admitting his actions driving through the busy pedestrian mall and along footpaths caused death and injury, he pleaded not guilty to six charges of murder and 27 of reckless conduct endangering life.

Earlier

A jury has begun deliberating in the murder trial of 28-year-old James "Dimitrious" Gargasoulas, who has admitted killing six people in a Bourke Street rampage.

Despite admitting his actions driving through the busy pedestrian mall and along footpaths caused death and injury, he has pleaded not guilty to six charges of murder and 27 of reckless conduct endangering life.

On Tuesday, barrister Theo Alexander delivered a short closing address to the jury, saying the defence was not challenging the prosecution case.

"Six people were killed, 27 people were injured. You've heard Mr Gargasoulas' plea and his explanation. You'll now hear from His Honour about the law," Dr Alexander said.

"On behalf of Mr Gargasoulas, I thank you for your attention."

Justice Mark Weinberg told jurors they must accept Gargasoulas' admissions as established facts.

He explained although Gargasoulas was suffering from mental health issues, he had not used mental impairment as a defence.

"Presumably he has taken the view that he could not establish the elements for that positive defence," Justice Weinberg told the jury.

He added that because Gargasoulas' psychosis and delusions at the time of the rampage were drug-induced, he could not argue he was not guilty by way of mental impairment.

On Monday, Gargasoulas told the Supreme Court he was sorry for his actions but neither his apology nor a lengthy sentence would change anything.

Gargasoulas took to the stand on Monday to say he hadn't intended for anyone to die, but understood that "in a sense, yes", he knew when he was doing it that was the probable outcome.

"I apologise from my heart but that's not going to fix anything ... neither will a lengthy sentence fix what I done," he told the jury.

He claimed he had a premonition half an hour before the Bourke St attack giving him permission to run people down in order to evade police, but that he didn't have permission to kill anyone.

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