In this paper, using the bargaining game theory, we propose a bandwidth management scheme that allocates bandwidth in an efficient and proportionally fair manner between the service classes with different service requirements. Since the traffic input rates of the classes are asymmetric in most of the time, the proposed scheme allocates bandwidth in proportion to the traffic input rates to increase the bandwidth utilization while protecting the quality of service of a class against the excessive traffic input of the other classes. In addition, the proposed method considers the weights of classes so that the bandwidth is allocated differentially among the classes.