A sports car worth almost a quarter of a million dollars was stolen at gunpoint in Sydney's north-east on Wednesday night, sparking a lengthy and erratic police chase, several days after the car was posted for sale online.

The white Audi R8, a V10 with automatic transmission, was advertised on several car websites a week and a half ago for $230,000.

Its owner, a 30-year-old Balgowlah man, said the 2014 model in "ibis white" with red seats had driven 25,000 kilometres and had never been taken on a racing track.

He was contacted by a "prospective buyer" who arranged to meet him outside a service station on Sydney Road in Balgowlah at 6pm on Wednesday.

The pair went on a test drive in the area, with the owner behind the wheel, but when they got to Castle Circuit in Seaforth, the passenger pulled out a gun.

Police said the driver was threatened with the gun, then pistol-whipped in the head, causing a cut over his left eye. He was then forced from the car before the other man drove away.

The car's owner called police and was taken to Manly Police Station, where he was treated by paramedics.

Police said a description of the car was broadcast to officers in the area, and the sedan - NSW registration DCL 86X - was spotted soon after on Military Road in Mosman. Police began a pursuit.

With officers in tow, the stolen car drove erratically southbound through the Sydney Harbour Tunnel, through the inner city including the Woolloomooloo area, then turned and drove back through the Harbour Tunnel.

It then drove through the Lane Cove Tunnel, onto the M2 motorway and then onto Pennant Hills Road at Beecroft, police say.

The Audi rammed a police car and damaged several other cars during the pursuit.

"Police were forced to terminate the pursuits several times due to the high-risk behaviour of the driver. Several cars have been damaged in minor collisions with the stolen vehicle and a police car rammed," police said in a statement.

Mobile phone vision from the Domain car park in the CBD showed several people standing next to a damaged car with its hazard lights on as police arrived on the scene.

The man who stole the car is described as being of Mediterranean/Middle Eastern appearance with a thin build, possibly aged in his early 20s, with hair that is shaved at the sides and long on the top.

At the time the car was stolen he was wearing a long, black leather jacket, black shirt and pants and white sneakers.

Police say anyone who sees the man or the car should not approach it and should call triple zero immediately.