In a nonvolatile semiconductor memory device in which a plurality of threshold values are set to store multi-level data in a memory cell, bits of multi-bit data are separately written into a memory cell according to an address signal or a control signal to effect the reading and erasing. Concretely, the memory array is so constituted that it can be accessed by three-dimensional address of X, Y and Z, and multi-bit data in the memory cell is discriminated by the Z-address.