There is disclosed a semiconductor memory device comprising a memory cell connected to a bit line, and a clamp circuit comprising a load MOS transistor connected between a power source voltage and the bit line, for clamping the power source voltage and applying the clamped voltage to the bit line. The semiconductor memory device further comprises a bypass circuit connected between the bit line and a reference voltage, for bypassing from the bit line to the reference voltage an electric current the amount of which is substantially equal to that of a weak inversion current of the load MOS transistor flowing into said bit line.