Emergency services were called after a black Kia Rio collided with the man who was pushing a pram at the time.
The 63-year-old, believed to the grandfather, suffered serious injuries whilst the two children also sustained injuries believed to be minor.
A spokesperson for Northumbria Police said: "At around 10.50am today, police received a report of a collision on Park Avenue, Whitley Bay.
"Officers attended the scene where a black Kia Rio has collided with a man and a pram.
"The 63 year-old man has been taken to hospital with serious injuries not believed to be life threatening.
"Two children – a one-year-old and two-year-old – have been taken to hospital with minor injuries.
"The driver of the car remained at the scene and is helping with enquiries."