Resource management is critical to the usability and accessiblity of grid computing systems. Conventional approaches to grid resource discovery are either centralized or hierarchical, and these prove to be inefficient as the size of the grid system increases. The Peer-to-Peer (P2P) paradigm has been applied to grid systems as a mechanism for providing scalable range-query and multi-attribute resource management. However, most current P2P-based resource management approaches support multi-attribute range queries at a high cost. They either depend on multiple P2P networks with each P2P network responsible for a single attribute, or they keep the resource information of all attributes in a single node. This paper presents a low-overhead range-query multi-attribute P2P-based resource management approach, LORM. Unlike other P2P-based approaches, it relies on a single P2P network and allocates resource information to different nodes based on resource attributes and values. Moreover, it has high capability to handle the large-scale and dynamic characteristics of resources in grids. Simulation results demonstrate the efficiency of LORM in comparison with other resource management approaches in terms of resource management overhead and resource discovery efficiency.