A semiconductor memory device includes memory cell transistors and a control circuit. The control circuit is configured to set a threshold voltage of each memory cell transistor to be in one of voltage ranges to store multi-bit data in each memory cell transistor. The voltage ranges include a first range corresponding to a first multi-bit value, a second range lower than the first range and corresponding to a second multi-bit value, and a third range that is the lowest. When a target memory cell transistor in which data of the second multi-bit value is to be written currently stores data of the first multi-bit value, the control circuit is configured to apply a first voltage to a gate of the target memory cell transistor, to shift the threshold voltage of the target memory cell transistor to be in the second range without dropping into the third range.