UPDATE 12.45pm: Police have confirmed the injured driver of the Peugeot 107 was a 19-year-old girl from Falmouth.
She suffered severe pelvic and head injuries in the crash.
Three other vehicles were involved - a VW Transporter van, a Renault Trafic van and a Nissan Primastar van, all registered to the Truro area.
The Serious Collisions Investigation Team are on site carrying out a detailed investigation, but the road has been reopened.
UPDATE 12.25pm: Traffic is still heavy on the A39, both ways between Greenbank Road and the A393 because of the earlier accident, but all lanes have now reopened.
UPDATE 11am: There are still serious problems on the roads around Poonsanooth and on the A39 due to an earlier accident.
One Twitter user reports that all roads to Falmouth are blocked, with a small crash on the Stithians road causing further problems.
UPDATE 10am: The injured woman has been airlifted to Derriford Hospital by an RNAS Culdrose Sea King Helicopter
The A39 remains closed following the accident, which took place at 7.30am.
Police say the road will remain closed for some time. Diversion are in place and drivers are requested to avoid the area.
Witnesses to the accident can contact the police on 101, quoting reference 66 of 26/03/13.
BREAKING 8am: A serious accident has blocked the A39 on the Mylor turn near the Norway Inn. The road has been closed.
Two vans and a car are involved. Traffic is queuing back up towards Devoran and Penryn.
Eyewitnesses report that a woman is being cut out of a blue car by the emergency services. It was thought the vehicle was in collision with a white van.
The van is then said to have collided head on with a black van heading towards Truro.
The blue car ended up in the front garden of a house where firefighters had to remove the roof to remove the occupant, thought to be a young woman in her 20s, eyewitnesses say.