Police will have to wait to speak to a driver who is in an induced coma after his four-wheel-drive crashed twice in Sydney's eastern suburbs this morning.

The driver, a 34-year-old man, is in a critical condition in the intensive care unit of St Vincent's Hospital after the crashes on Anzac Parade at Moore Park about 12.30am, hospital spokesman David Faktor said.

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The man was driving south on Anzac Parade in a Nissan Navara when he hit the back of a Honda Civic, Inspector Paul Kelly of Surry Hills Local Area Command said.

Instead of exchanging contact details with the Honda Civic driver, he sped away and tried to turn on to Cleveland Street, Inspector Kelly said.

But he lost control of his car and hit a taxi at the traffic lights. The impact caused the taxi to collide with another car near it, he added.

The Navara flipped on to its hood and the driver was trapped in it. He was freed by officers from Police Rescue, treated by paramedics and taken to St Vincent's.

The Honda Civic driver was taken to the same hospital but released, Inspector Kelly said.

Investigators were awaiting the results of blood tests from the Navara and Civic drivers.

Inspector Kelly said the taxi driver and the driver of the car hit by the taxi returned negative drug and alcohol tests at the crash site.

Police appealed for anyone with information to phone Crime Stoppers on 1800 333 000.