A semiconductor memory device according to an embodiment comprises a memory cell and a control circuit, the control circuit performing write of data to the memory cell. The memory cell includes a second resistance varying layer sandwiched between a first resistance varying layer and a third resistance varying layer. The second resistance varying layer has a resistance value which is smaller than that of the other resistance varying layers. The control circuit applies to the memory cell a first voltage pulse, and then applies to the memory cell a second voltage pulse that has a rise time which is shorter than that of the first voltage pulse.