According to one embodiment, a semiconductor memory device includes memory cell arrays each including blocks. The block is unit of erase and includes string-groups. Each string-group includes strings each including a first transistor, memory cell transistors, a second transistor coupled in series. The first transistor is connected to different bit line and the second transistor is connected to same source line. The memory cell arrays are provided with different respective block address signals. The memory cell arrays are provided with different respective string address signals. Each of the block address signals specifies one block. Each of the string address signals specifies one string-group.