A semiconductor memory has a memory cell array having dynamic memory cells. An access control circuit accesses the memory cells in response to an access command which is supplied externally. A refresh control circuit generates, during a test mode, a test refresh request signal in synchronization with the access command so as to execute a refresh operation of the memory cells when a refresh mask signal is at an invalid level. Also, the refresh control circuit prohibits generation of the test refresh request signal when the refresh mask signal is at a valid level. The test refresh request signal is generated or prohibited from being generated according to the level of the refresh mask signal. Thus, only a refresh operation needed for a test can be executed, and hence test efficiency can be improved.