Donna J. Potter, 44, of Bear was killed in the crash that happened at 8:16 p.m. Thursday along the 700 block of Pulaski Highway.
Police say Potter, who was walking her dog, attempted to cross the busy highway and was struck in the westbound lanes.
Medics responded and rushed Potter to Christiana Hospital where she died.
Her dog was taken to an area animal hospital for care.
The driver of the SUV remained at the scene and was not injured.
No charges have been filed as this investigation continues.