Flow control algorithm in high speed networks is a resource-sharing policy implemented in a distributed manner. This paper introduces a novel concept of backlog balancing and demonstrates its application to network flow control and congestion control by presenting a rate-based flow control algorithm for ATM networks. The aim of flow control is to maximize the network utilization for achieving high throughput with tolerable delay for each virtual circuit (VC). In a resource-sharing environment, this objective may also cause network congestion when a cluster of aggressive VC's are contending for the same resource at a particular node. The basic idea of our algorithm is to adjust the service rate of each node along a VC according to backlog discrepancies between neighboring nodes (i.e., to reduce the backlog discrepancy). The handshaking procedure between any two consecutive nodes is carried out by a link-by-link binary feedback protocol. Each node will update its service rate periodically based on a linear projection model of the flow dynamics. The updated service rate per VC at a node indicates its explicit demand of bandwidth, so a service policy implementing dynamic bandwidth allocation is introduced to enforce such demands. Simulation study has validated the concept and its significance in achieving the goal of flow control and yet preventing network congestion at the same time.