Bandwidth is an extremely valuable and scarce resource in multimedia networks. Therefore, efficient bandwidth management is necessary in order to provide high Quality of Service (QoS) to users. In this paper, a new QoS-aware bandwidth allocation algorithm is proposed for the efficient use of available bandwidth. By using the multi-objective optimization technique and Talmud allocation rule, the bandwidth is adaptively controlled to maximize network efficiency while ensuring QoS provisioning. In addition, we adopt the online feedback strategy to dynamically respond to current network conditions. With a simulation study, we demonstrate that the proposed algorithm can adaptively approximate an optimized solution under widely diverse traffic load intensities.