The crash happened at 10.45am on Saturday, on South Marine Drive.
Police said two pedestrians were struck by a blue Peugeot 308 as it left the road.
Both were taken to Hull Royal Infirmary for treatment for serious injuries.
One of the victims, a 70-year-old man, died of his injuries.
A 70-year-old woman remains in hospital.
The driver of the Peugeot was taken to Scarborough Hospital for treatment and has since been discharged.
Police said a front seat passenger of the car also sustained minor injuries, but three back-seat passengers were not hurt in the collision.
Anyone with information is asked to call police on 101, quoting log 247 of July 8 2017.