Emergency services were called to the scene between Findon and Clapham just before 9.30am where police say a black Chrysler Voyager, travelling south, had collided with a northbound white Toyota Aygo.
The driver of the Chrysler, a 25-year-old man from Crawley, and his passenger suffered minor injuries, police said.
But the 60-year-old driver of the Toyota, a woman from Rustington, suffered multiple serious injuries and was taken to the Royal Sussex County Hospital in Brighton.
The road was closed while rescue, recovery and collision investigation work took place and was re-opened at around 3.30pm.
Anyone who witnessed the collision who has not spoken to police or anyone who has dashcam footage of either vehicle in the time leading up to it is asked to report online or call 101 quoting Operation Envelope.
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