A network relaying apparatus and method for high quality transfer of packets under stable quality-of-service (QoS) control. A transfer engine stores the packets received through a network interface, in a packet buffer, and the header information in a RAM. A search engine searches the transfer control information including the transfer destination information and the action information according to the header information and writes the resulting information in the header RAM. The transfer engine produces an output packet based on the information stored in the packet buffer and the header RAM and outputs it to the transfer destination. A switch operates to switch the output packet to the routing processor of the destination. The QoS control is performed at each of a plurality of points including the input-side routing processor, the output-side routing processor 10 and the switch.