Hudson, 31, this morning pleaded guilty in Melbourne Magistrates Court to one count of murder, two of attempted murder and one of intentionally causing serious injury.

He was accused of killing father-of-three Brendan Keilar, 43, and wounding two others - Kara Douglas and Paul de Waard - during the morning peak-hour rush in the city.

Miss Douglas lost a kidney after she was shot by Hudson. Mr de Waard, a Dutch backpacker was shot twice in the chest and stomach as he tried to help Ms Douglas, who was struggling with Hudson before the shooting.

Wearing a grey pin-striped suit, cream shirt and pink tie, Hudson sat in the dock with his hands clasped as he admitted to the murder of Mr Keilar and the attempted murder of Miss Douglas and Mr de Waard.

He appeared calm and looked at Magistrate Phillip Goldberg for most of the short hearing.

Magistrate Goldberg struck out a charge of unlawful imprisonment against Hudson.

He ordered Hudson, who did not apply for bail, to face a Supreme Court directions hearing on June 2.