A controller with a buffer is provided between a main memory and an external storage. This controller supplies a given request for access to the external storage and issues a preload request for a retrieval extent of the next access request by the time when data associated with this first access request is completely transferred to the buffer memory or to the main memory. Moreover, the controller stores the preloaded data in the buffer and, for the next access request, it transfers the data stored in the buffer to the main memory. Therefore, even when the host side (CPU) is processing, the access to the external storage can be made simultaneously, thus the response time and the operating ratio of the computer system being improved.