While a plurality of physical address memories are provided with respect to one logical address of a non-volatile memory device, an empty physical address memory contained in the plural physical address memories is searched with respect to a writing operation for one logical address, and then, data is written in this empty physical address memory. With respect to a reading operation for one logical address, such a physical address memory to which data has been written at last is searched, and the storage content of this memory is read out. As a result, the data rewriting operation to a non-volatile memory can be carried out with employment of the simple circuit arrangement with respect to one logical address, while an erasing operation is not performed, and an area of a memory device is not increased but also a total number of data rewriting operation is not limited to a number defined in a specification of the memory device.