An internal row address signal is generated by a refresh address counter and supplied to a row decoder. In a normal refresh operation, the refresh address counter sequentially increments the internal row address signal on the basis of a trigger signal. As a result, the data in all memory cells is refreshed. In a low-consumption-current refresh operation, at least one of the bits of the internal row address signal is fixed. Hence, the refresh operation is executed only for the memory cells of a predetermined refresh area.