The accident happened in the 800 block of Barbeque Church Road in Sanford, on the Lee-Harnett County line Monday evening.
Troopers say the car ran off the road, overcorrected and hit the end of the guardrail on the bridge.
State Highway Patrol troopers say the driver, 24-year-old Raheem Miller, was taken to Cape Fear Valley Medical Center where he was last listed in critical condition.
A passenger, 53-year-old Gordon Harrington, was taken to WakeMed. He was listed in stable condition.