The crash happened at about 4.40pm on Thursday, in the car park at Asda supermarket, in Holt Lane, Holt Park.
Police said an 82-year-old man was involved in a collision with a Mercedes Vito car.
He was knocked to the ground, and taken to Leeds General Infirmary where he remains in a critical condition.
Officers are appealing for any witnesses to the incident or anyone who has any information about the collision.
Anyone with any information is asked to contact the police via 101, quoting log number 1299 of October 26.