A router for supporting differentiated qualities of service (QoS), and a fast Internet protocol (IP) packet classification method performed in the router, are provided. The router hierarchically divides a memory having flow tables into a fast internal cache memory and an external typical memory. The internal cache memory stores recently searched table entries. The router preferentially searches the flow tables of the internal cache memory. Only when the internal cache memory searching fails, the flow tables of the external memory are searched. Consequently, the frequency of interactions between a packet classifier and the external memory decreases to improve the speed of packet classification.