A semiconductor memory system including a flash EEPROM comprises a first flash EEPROM included in the first memory drive, a second flash EEPROM included in the second memory drive, and means for controlling access to the first and second flash EEPROMs. The access controlling means includes an address converting means for converting a logical address from a host system into a physical address, according to first and second file management information which indicates correspondence between logical addresses and physical addresses of the first and second memory drives, respectively. The access controlling means further includes memory accessing means, coupled to each of the first and second flash EEPROMs, for accessing a selected EEPROM according to the physical address from the address converting means.