1. A wear leveling method, for a multi level cell (MLC) NAND flash memory, wherein the MLC NAND flash memory comprises a first zone having a plurality of blocks and a second zone having a plurality of blocks, and each of the blocks in the first zone and the second zone comprises an upper page and a lower page, the wear leveling method comprising: determining whether to start a block swapping operation of a wear leveling process in the first zone of the MLC NAND flash memory according to a first start-up condition; determining whether to start the block swapping operation in the second zone of the MLC NAND flash memory according to a second start-up condition, wherein the first start-up condition is different from the second start-up condition; when the first start-up condition is met, performing the block swapping operation in the first zone; and when the second start-up condition is met, performing the block swapping operation in the second zone, wherein the blocks in the first zone are accessed by using only the lower pages, and the blocks in the second zone are accessed by using both the lower pages and the upper pages.