A non-volatile memory (NVM) apparatus and an iteration sorting method thereof are provided. The NVM apparatus performs the iteration sorting method to select one target block from a plurality of blocks of a NVM, and to perform a management operation on the target block. The iteration sorting method includes: selecting a plurality of candidate blocks among the blocks of the NVM to join into a sorting set, sorting all of the candidate blocks in the sorting set according to metadata, picking one candidate block with maximum (or minimum) metadata from the sorting set to serve as the target block, and keeping M candidate blocks in the sorting set and discarding the rest of the candidate blocks from the sorting set.