A semiconductor memory device includes a memory cell array where a plurality of memory cells are arranged in a matrix, each of the memory cells serially connecting a two-terminal type memory element and a transistor for selection, a first voltage applying circuit that applies a write voltage pulse to a bit line, and a second voltage applying circuit that applies a precharge voltage to a bit line and a common line. In writing the memory cell, after the second voltage applying circuit has both terminals of the memory cell previously precharged to the same voltage, the first voltage applying circuit applies the write voltage pulse to one terminal of the writing target memory cell via the bit line, and while the write voltage pulse is applied, the second voltage applying circuit maintains the application of the precharge voltage to the other terminal of the memory cell via the common line.