1. A data storing method for a rewritable non-volatile memory module, the rewritable non-volatile memory module has a plurality of physical erase units, and each of the physical erase units has a plurality of physical program units, the data storing method comprising: configuring a plurality of logical addresses, and dividing the plurality of logical addresses into a plurality of logical zones; respectively establishing a plurality of logical address mapping tables for the plurality of logical zones, wherein each of the logical zones is corresponding to one logical address mapping table; receiving data from a host system, wherein the data is stored to a first logical address among the plurality of logical addresses according to an instruction of the host system; writing the data into a first physical program unit among the physical program units of the plurality of physical erase units; recording a mapping record indicating that the first logical address is mapped to the first physical program unit in a temp mapping table; determining whether the temp mapping table is full; and if the temp mapping table is full, updating mapping relations between the plurality of logical addresses and the physical program units of the plurality of physical erase units in the plurality of logical address mapping tables based on a plurality of mapping records recorded in the temp mapping table, and deleting the plurality of mapping records recorded in the temp mapping table, wherein the mapping relations of a portion of the physical program units among the plurality of physical program units of the plurality of physical erase units are recorded in the temp mapping table.