The camera based Automatic Number Plate Recognition will be introduced in October after the Morrisons store received complaints from shoppers and visitors unable to find a space.
Although the 400 space car park has had a three hour limit since 2012 it has not been monitored.
The new system will be effective from 9am-5pm each day and those staying over three hours will be fined.
However, there will be some free parking permits are being made available to local traders and the neighbouring doctors’ surgery which can be arranged through Leeds Council.
Store manager, Paul Kelly said: “The car park has always been very well used and finding a space was difficult. Many drivers continued to overstay and shoppers told us that they were still finding it hard to park.”