In an FCRAM having a late write function, when a first command signal indicates "write active", whether a write operation or an auto-refresh operation is to be performed is determined on the basis of a second command signal. For example, when the second command signal indicates "write", a write operation for a memory cell is performed by a late write scheme. When the second command signal indicates "auto-refresh", an auto-refresh operation is performed. In the last write cycle of a write operation immediately preceding this auto-refresh operation, addresses for selecting a memory cell as an object of auto-refresh are predetermined. After data write to a memory cell is completed in the last write cycle, row precharge for auto-refresh is performed. After that, an auto-refresh operation (i.e., a data read operation and a data restore operation) is performed for the selected memory cell.