A communication controller comprises a storage for storing data of a message being received, a determining unit for determining types of the message being received, and a transmission controller for generating interrupt requests for transferring data to a data processing unit at a different timing responsive to determination by the determining unit. That is, if the message being received requires immediate processing, the transmission controller immediately transmits an interrupt request signal to a CPU. The CPU then reads from the storage not only the data which require urgent processing but also all the data stored in the storage, and stores the data in its memory. If the message does not require immediate processing, the transmission controller transmits the interrupt request signal to the CPU when the data stored in the storage have reached a predetermined amount or when a predetermined time has elapsed from a time that the data began to be stored in the storage.