The semiconductor memory device can continuously read or store a plurality of data therefrom or therein. The semiconductor memory device includes a memory unit having a plurality of memory cells (3,4), the memory cells being arranged in a matrix having rows and columns, and a reading storing circuit. The reading storing circuit can read or store data from or into the memory cell at an address corresponding to an address signal received therein in response to the reception of first and second control signals, respectively. The reading storing circuit also can consecutively read or store data from or into the memory cell at another address subsequent to the address read or stored at the last time in response to the reception of the second control signal. Such a device can therefore have improved access time for continuous accessing of a plurality of data.