The 33-year-old was crossing the road when he was struck by a black BMW 325 on Black Bull Street. He died at the scene.
The collision happened at 9.40pm on Friday night.
The driver, a 25-year-old man, has been arrested on suspicion of causing death by dangerous driving and remains in custody.
Officers are appealing for anyone who saw what happened and in particular the driver of the car who was following the car in the collision to come forward and contact police via 101 or use the contact us options at www.westyorkshire.police.uk quoting log number 1941 of October 12.