According to one embodiment, a semiconductor memory device includes a semiconductor substrate, a plurality of memory cells, a plurality of wires, and a control circuit. The control circuit allows a first current to change a state to flow on a selected cell by applying a first potential difference between a pair of wires that sandwich the selected cell selected from the plurality of memory cells with respect to the semiconductor substrate vertically, and allows a second current lower than the first current to flow on an non-selected cell in the same direction as the direction of the first current by applying a second potential difference between a pair of wires that sandwich the non-selected cell connected to a wire shared with the selected cell on a different layer from the selected cell.