Multi-constraint quality-of-service routing has become increasingly important as the Internet evolves to support real-time services. Restricted shortest path (RSP) is one of the important problems studied in the field of QoS routing. Various solutions have been proposed for RSP and other problems related to the QoS routing, in practical situations. Restricted shortest path problem with concave route costs are studied in this paper. This is a special version of the traditional RSP problem and is widely applicable in wireless and mobile ad hoc networks. In this paper, we propose new algorithms for this kind of routing. The effectiveness of our proposed solutions is shown through analytical reasoning and simulations.