Now that cellular networks are being called upon to support real-time interactive multimedia traffic such as video teleconferencing, these networks must be able to provide their users with quality-of-service (QoS) guarantees. Although the QoS provisioning problem arises in wireline networks as well, mobility of hosts, scarcity of bandwidth, and channel fading make QoS provisioning a challenging task in wireless networks. It has been noticed that multimedia applications can tolerate and gracefully adapt to transient fluctuations in the QoS that they receive from the network. The management of such adaptive multimedia applications is becoming a new research area in wireless networks. As it turns out, the additional flexibility afforded by the ability of multimedia applications to tolerate and adapt to transient changes in the QoS parameters can be exploited by protocol designers to significantly improve the overall performance of wireless systems. The main contribution of this paper is to propose a novel, rate-based, borrowing scheme for QoS provisioning in high-speed cellular networks carrying multimedia traffic. Our scheme attempts to allocate the desired bandwidth to every multimedia connection originating in a cell or being handed off to the cell. The novelty of our scheme is that, in case of insufficient bandwidth, in order not to deny service to requesting connections (new or hand-off), bandwidth will be borrowed, on a temporary basis, from existing connections. Our borrowing scheme guarantees that no connection gives up more than its fair share of bandwidth, in the sense that the amount of bandwidth borrowed from a connection is proportional to its tolerance to bandwidth loss. Importantly, our scheme ensures that the borrowed bandwidth is promptly returned to the degraded connections. Extensive simulation results show that our rate-based QoS provisioning scheme outperforms the best previously known schemes in terms of call dropping probability, call blocking probability, and bandwidth utilization.