Unstructured peer-to-peer (P2P) systems (e.g. Gnutella) are characterized by uneven distributions of node connectivity and file sharing. The existence of “hub” nodes that have a large number of connections and “generous” nodes that share many files significantly influences performance of information search over P2P file-sharing networks. In this paper, we present a novel Scalable Peer-to-Peer Search (SP2PS) method with low maintenance overhead for resource discovery in scale-free P2P networks. Different from existing search methods which employ one heuristic to direct searches, SP2PS achieves better performance by considering both of the number of shared files and the connectivity of each neighbouring node. SP2PS enables peer nodes to forward queries to the neighbours that are more likely to have the requested files and also can help in finding the requested files in the future hops. The proposed method has been simulated in different power-law networks with different forwarding degrees and distances. From our analytic and simulation results, SP2PS achieves better performance when compared to other related methods.