A semiconductor memory device for reducing ripple noise of a back-bias voltage, and a method of driving the semiconductor memory device include a word line driving circuit and a delay logic circuit. The word line driving circuit enables a sub-word line connected to a selected memory cell to a first voltage, and disables the sub-word line of a non-selected memory cell to a second voltage and a third voltage, in response to a sub-word line enable signal, a first word line driving signal, and a second word line driving signal. The delay logic circuit controls the semiconductor memory device so that an amount of charge of the sub-word line that is introduced to the third voltage is greater than an amount of charge of the sub-word line that is introduced to the second voltage by changing a transition point of time of the sub-word line enable signal with respect to a transition point of time of the first word line driving signal, during the disabling of the sub-word line.