A semiconductor memory device includes a memory cell array in which a plurality of memory cells is aligned in a matrix shape, each memory cell including a two-terminal memory element and a transistor for selection connected in series; a first voltage applying circuit that applies a writing voltage pulse to first bit lines; and a second voltage applying circuit that applies a pre-charge voltage to the first bit lines and second bit lines, wherein in a writing of a memory cell, after the second voltage applying circuit has pre-charged both ends of the memory cell to a same voltage, the first voltage applying circuit applies the writing voltage pulse via the first bit line that is directly connected to the transistor for selection, and the second voltage applying circuit applies the pre-charge voltage to the second bit line directly connected to the memory element.