In a magnetic tape storage including a nonvolatile buffer memory, the buffer memory memorizing sets of data sent from a host computer, a set of data including a pair of one file and one tape mark, the tape mark showing the end of the file, sets of data are continuously stored in the buffer memory until the total data amount of the sets of data comes up to a predetermined data amount, and the sets of data stored in the buffer memory are wrote to a magnetic tape (called flushing) when the total data amount of the sets of data in the buffer memory exceeds the predetermined data amount. The frequency of the flushing and tape reposition according to the flushing can be greatly decreased. The wear-out of the magnetic tape and mechanical section relating to the magnetic tape running in the storage can be reduced.