A semiconductor memory device that does not delay read/write access due to a refresh and can be interface compatible with a high-speed SRAM such as a QDR SRAM, comprises a plurality of subarrays each having a plurality of dynamic memory cells; at least one cache memory for the plurality of subarrays; a circuit to check whether data read from the subarray selected by a read address is present in the cache memory or not; and a circuit performing control so that the check result indicates that the data is present in the cache memory, the data is read from the cache memory and refreshing of the subarray is performed concurrently with a read cycle.