Recently, as multimedia and high-speed traffic become more popular on the Internet, the various traffic requiring different qualities of service (QoS) will co-exist. In addition, classified service based on Diff-Serv (Differentiated Service), MPLS (Multi-Protocol Label Switching),etc., have come into wide use. Today's Internet environment requires routers to perform control mechanisms in order to guarantee various QoSs. In this paper, we propose a buffer management scheme for the Internet router that uses class-based priority control. This paper focuses on per-flow queueing, and evaluates the performance of the proposed buffer management scheme. Realization of differentiated services and dissolution of buffer occupation by specific flow is expected by the proposed control.