The identity of a jogger remains a mystery after he was struck by a car and left in a critical condition on Sunday afternoon.

He remained in a coma with serious head injuries on Monday morning, after he was hit by a car while trying to cross a main road at Punchbowl.

Police say they believe the man was running at the time and have no idea who he is because he was not carrying any identification

"He is believed to have been jogging," a NSW police spokesman said.

"We are keen to identify him and anyone else that may have witnessed [the incident]," he said.

The man was trying to cross Canterbury Road when he was hit by a white Toyota sedan about 4.30pm, police said.

The force of the impact propelled the man into the driver's side window of the car, leaving it completely shattered.

Police blocked off traffic near the intersection with Cullens Road and did first aid until paramedics arrived.

He was taken to St George Hospital where he was placed in an induced coma in a critical condition.

The driver was spoken to by police and taken to Canterbury Hospital for mandatory blood and urine tests.

Police urge anyone who saw anything prior to or at the time of the incident, to call Crime Stoppers on 1800 333 000.