An Australian man rammed his four-wheel drive into a Sydney police car, hijacked a supermarket delivery truck and taxi, rammed other cars and stabbed and wounded a passerby before killing himself in front of police on Friday.

The dramatic chain of events, which police said was not terror-related, began when police tried to pull over the four-wheel drive for not displaying licence plates.

The driver rammed the police car, dumped the four-wheel drive and hijacked a supermarket delivery truck about 7km away, then continued across town for another 20km to a suburb near the airport, hitting several cars along the way.

The driver, 24, tried to steal another car, stabbing a passerby who tried to stop him, before stealing a taxi.

Police finally stopped the attacker in the taxi and tried to Taser him, but the man stabbed himself in the chest and died at the scene.

"The offender wasn't trying to intentionally harm people," Acting Assistant Commissioner Mick Fitzgerald told reporters in Sydney.

"It was a man who was attempting to do everything he could to avoid arrest. His actions, in particular the actions when he stabbed the innocent person, (are) the actions of a person who we believe had mental health problems."

Police did not identify the attacker or give further details. Fitzgerald said the man was known to police and did not have a significant criminal history.

Footage circulated on social media showed a man in a beige shirt and cap gesturing for a taxi driver to get out of his car, then getting in and driving the red taxi away.

The Australian Associated Press (AAP) quoted a tradesman who witnessed the first stabbing, Chris Burton, as saying the attacker looked "crazy and frazzled".

"He goes to the guy, 'stab me, stab me, stab me' and stuck his neck out," AAP quoted the witness as saying.

The passerby who was stabbed was in a serious but stable condition in hospital, police said. Media reported that a woman was also stabbed in the melee but police did not confirm a second stabbing.

A staunch US ally, Australia has been on alert for militant attacks after a Sydney cafe siege in 2014 and its intelligence agencies have stepped up scrutiny.

In November, a man set fire to a pickup truck laden with gas cylinders in Melbourne and stabbed three people, killing one, before being shot by police. Police described that rampage as an act of terrorism.