A synchronous memory device can reduce unnecessary current consumption in its operation. In the synchronous memory device, a clock receiver receives an external clock to output a first internal clock. An address latch unit receives and latches an address in synchronous with the first internal clock. A row address latch unit latches a row address that is outputted from the address latch unit. A column address control unit receives the first internal clock to output a second internal clock and stops the output of the second internal clock when a non-column command is performed. Finally, a column address control unit is activated in response to the second internal clock to count a column address that is outputted from the address latch unit so as to output an inner column address.