Discovering an available relaying path is a critical prerequisite for the success of the multi-hop cellular networks. Since forwarding data for others utilizes the resources of the mobile nodes such as battery energy, link bandwidth, buffer space and processing time, the mobile nodes may accept only a certain number of relaying requests. In this paper, we propose a Quality of Relay (QoR)-based routing scheme to select a routing path between a mobile node and the central base station based on the individual importance of each intermediate node contributing to hop-by-hop connections. The proposed routing scheme can retain more valuable resource for later relaying requests, thereby supporting more connections successfully. Simulation results indicate that the proposed routing scheme causes a lower new call blocking probability than the shortest-path routing scheme under a certain constraint on maximum relaying capacity of each mobile node.