A semiconductor memory device includes a DRAM, an SRAM and a bi-direction transfer gate circuit provided between SRAM and DRAM. SRAM array includes a plurality of sets of word lines. Each set is provided in each row of SRAM array and each word line in each set is connected to a different group of memory cells of an associated row. An address signal for the SRAM and an address signal for the DRAM are separately applied to an address buffer. The semiconductor memory device further includes an additional function control circuit for realizing a burst mode and a sleep mode. A data transfer path from DRAM to the SRAM and a data transfer path from the SRAM to the DRAM are separately provided in the bi-directional transfer gate circuit. Data writing paths and data reading paths are separately provided in the DRAM array. By the above described structure, operation of the buffer circuit is stopped in the sleep mode, reducing power consumption. Since data writing path and data reading path are separately provided in the DRAM array, addresses to the DRAM array can be applied in non-multiplexed manner, so that data can be transferred at high speed from the DRAM array to the SRAM array, enabling high speed operation even at a cache miss.