A storage control apparatus contains plural request stacks for storing the access request; a stack selecting circuit for selecting a request stack by accepting the access requests one after another and for storing the access request; and a priority determining circuit for selecting the access request stored in said request stack in order of priority and makes access to a main storage unit in response to an access request from an input-output processor, instruction processor and the like. When memory access requests are issued continuously from the unit as a source of issuing the same access request to the storage control apparatus, the access request which follows can make access to a cache memory while the previous request is making access to the main storage unit, thereby preventing a reduction in a total throughput.