A semiconductor memory device, for performing a writing operation faster without expanding a driver for the writing operation, includes a bit line sense amplifier (BLSA) for sensing and amplifying a value in a bit line pair, a supply line driver for driving a supply line of the BLSA, a driving controller for controlling the supply line driver in response to a sense amplifier enabling signal, and a sense amplifier enabling signal generator for generating the sense amplifier enabling signal, which is activated based on active and precharge command signals and inactivated during a predetermined part of an writing operation. A driving method of a semiconductor memory device includes enabling the BLSA in response to an active command signal, disabling the BLSA during a predetermined part of an writing operation, enabling the BLSA after the predetermine part, and disabling the BLSA in response to a precharge command signal.