A man accused of murdering six people when he allegedly rampaged through Melbourne's CBD in a car is due to face the Supreme Court of Victoria.

Dimitrious Gargasoulas, 28, has previously pleaded not guilty to the accusations, along with 28 counts of attempted murder.

Gargasoulas has waived his right to a pre-trial committal hearing, so his case will be dealt with directly by the Supreme Court.

However, concerns have been raised throughout the proceedings over his mental health and his fitness to plead.

A hearing could be held in the Supreme Court before a jury to decide if he is fit to stand trial.

If found unfit, he would face a special hearing instead of a criminal trial to determine whether he is not guilty due to mental impairment.

Gargasoulas is scheduled due to appear before Justice Lex Lasry on Thursday for a mention and directions hearing.

© AAP 2018