A nonvolatile semiconductor memory device comprises a memory cell array including first and second mutually crossing lines and electrically erasable programmable memory cells arranged at intersections of the first and second lines, each memory cell containing a variable resistive element; a data write circuit operative to apply a voltage required for data write to the memory cell via the first and second lines; and a current limit circuit operative to limit the value of current flowing in the memory cell on the data write at a certain current limit value.