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In recent years, overlay networks have emerged as an approach to provide a general framework for new applications and services to be implemented without significant changes in the IP-layer network infrastructure. Overlay Service Network (OSN) is a unified framework which acts as a top layer over the IP-layer network and makes overlay routing feasible. This paper mainly focuses on designing a QoS-satisfied dynamic overlay routing protocol based on OSN framework. While satisfying the QoS requirements, being a dynamic routing protocol enhances the reliability and performance of the routing. So the proposed algorithm not only satisfies the application QoS requirements, but also improves the routing performance. The goals are: (1) to discover an overlay path which fulfills the QoS requirements, as well as (2) balancing the computational capacity of the resources and at the same time, (3) enhance the performance of the overlay network. To achieve these goals, we propose a path selection algorithm called Modified Least-Cost Path (MLCP) algorithm. Our simulation experiments have shown that the proposed algorithm performs well in achieving QoS-satisfied overlay routing while maintaining the performance.