In an electrically erasable non-volatile semiconductor memory device, a plurality of non-volatile semiconductor memory cells are arranged in a matrix form and are connected to corresponding ones of row and column lines. In a data writing mode, a first voltage Vp at is applied to the column lines so that the drains of the memory cells are maintained at a drain potential, and a second voltage is applied to the row lines so that a sum level of the drain potential and the threshold voltage of the memory cell is not smaller than the floating gate potential of the memory cell.