A non-volatile semiconductor memory device, comprising: a non-volatile memory array, storing multi-values by setting a plurality of different threshold voltages for each memory cell, and a control circuit, controlling a write-in operation to the memory cell array. When data have been written into the memory cell, the control circuit selects an adjacent word line, uses an erasing level to perform write-in which is weaker than the data write-in, and verifies soft programming of the amount of one page, such that a narrow-banded erasing level distribution is realized in an adjacent memory cell.