A semiconductor memory device includes a voltage detector configured to detect a level of an external power supply voltage and an internal voltage generator configured to generate an internal voltage in response to an active signal and drive an internal voltage terminal with a driving ability corresponding to an output signal of the voltage detector. A method for operating the semiconductor memory device includes detecting a level of an external power supply voltage, based on a first target level, to output a detection signal; and generating an internal voltage in response to an active signal, and driving an internal voltage terminal with a driving ability corresponding to the detection signal.