Centralized or hierarchical administration of the classical grid resource discovery approaches is unable to efficiently manage the highly dynamic large-scale grid environments. Peer-to-peer (P2P) overlay represents a dynamic, scalable, and decentralized prospect of the grids. Structured P2P methods do not fully support the multi-attribute range queries and unstructured P2P resource discovery methods suffer from the network-wide broadcast storm problem. In this paper, a decentralized learning automata-based resource discovery algorithm is proposed for large-scale P2P grids. The proposed method supports the multi-attribute range queries and forwards the resource queries through the shortest path ending at the grid peers more likely having the requested resource. Several simulation experiments are conducted to show the efficiency of the proposed algorithm. Numerical results reveal the superiority of the proposed model over the other methods in terms of the average hop count, average hit ratio, and control message overhead.