The accident happened around 5:00 p.m. on Naamans Road near Concord Pike in Talleyville.
Police say a 49-year-old Kevin M. Truehart of Wilmington was hit by a vehicle going westbound on Naamans Road.
Investigators say the driver of that car, 23-year-old Jamisa Johnson of Bear, Del., tried to avoid Truehart but still struck him with the front end of the car.
Truehart was rushed to the hospital in critical condition.
Johnson managed to stop her car and remained at the scene, police said.
There was no immediate word on any charges as this investigation continues.