The 79-year-old pedestrian was struck by the vehicle in Highdown Drive, Littlehampton at about 10:15 GMT on Wednesday.
Sussex Police said the woman, who lived locally, was taken to Royal Sussex County Hospital in Brighton but died from her injuries.
The force has appealed for witnesses to contact officers.
The van driver, a 49-year-old man from Worthing, was unhurt in the crash.
An elderly woman has died in hospital after she was hit by a van in West Sussex.