A refresh signal is output in response to a refresh request generated at predetermined cycles, and a refresh operation is performed. The refresh operation ends when a conflict occurs between an access request and the refresh request. Consequently, an access operation corresponding to the access request can be started earlier with a reduction in access time. The access time can be reduced further by changing the end time of the refresh operation in accordance with the timing of supply of the access request. Since a test circuit for notifying the state of the refresh operation to exterior is formed, the operation margin of the refresh operation can be evaluated in a short time. As a result, it is possible to reduce the development period of the semiconductor memory.