A semiconductor memory device according to the embodiment comprises memory cells each having asymmetrical voltage-current characteristics, wherein the memory cell has a first state, and a second state and a third state of higher resistances than that in the first state, wherein the memory cell, (1) in the second state, makes a transition to the first state on application of a first voltage of the first polarity, (2) in the first state, makes a transition to the second state on application of a second voltage of the second polarity, (3) in the first state, makes a transition to the third state on application of a third voltage of the second polarity (the third voltage