A nonvolatile semiconductor memory device comprises a cell array having plural memory cells arranged in matrix, each memory cell including a variable resistor having a resistance reversibly variable to store data corresponding to the resistance of the variable resistor; a selection circuit operative to select a memory cell from the cell array; and a write circuit operative to execute certain voltage or current supply to the memory cell selected by the selection circuit to vary the resistance of a variable resistor in the selected memory cell to erase or write data. The write circuit terminates the voltage or current supply to the selected memory cell in accordance with resistance variation situation of the variable resistor in the selected memory cell when current flowing in the selected memory cell reaches a certain level appeared after the data erase or write.