A low power semiconductor memory device can reduce power consumption of the whole chip by activating a bit line sense amplifier and a sub word line driver for driving a selected memory cell array block. The low power semiconductor memory device comprises a plurality of memory cell array blocks, a plurality of sense amplifier arrays, a sub word line driver array and a block selecting activation control unit. The block selecting activation control unit selectively activates the sub word line driver and the sense amplifier for driving the memory cell array block corresponding to a block selecting address.