The woman was hit by a green DAF Tipper truck in Bridge Street, at the pedestrian crossing near to the junction with Cattle Market Street.
The 85-year-old was seriously injured and pronounced dead at the scene a short time later.
Police spoke to the truck driver, a 55-year-old man, at the scene.
A West Yorkshire Police spokesman said: "Shortly before 11am this morning (10/9) an 85-year-old female pedestrian was involved in a collision with a green DAF Tipper truck in Bridge Street, at the pedestrian crossing, near to junction with Cattle Market Street.
"She was seriously injured and was pronounced deceased at the scene a short time later.
"The driver of the truck, a 55-year-old man, stopped at the scene and has been spoken to by officers.
"Road closures were in place while the vehicle was recovered and the scene examined.
"Anyone who witnessed the incident is asked to contact West Yorkshire Police Major Collision Enquiry Team via 101 quoting 13180451159."