Peer-to-Peer (P2P) computing can be integrated into the resource discovery of grid system to resolve the problems incurred by the centralized mechanisms. The overlay network construction is an important issue in the P2P ?based resource discovery systems. The traditional Gnutella-like method to construct the overlay network cannot guarantee the full connection of the overlay network. This paper proposes the OFM (Order Firstly Mode) technology. OFM builds an efficient overlay network by actually measuring the network delay among the grid nodes. Moreover a strategy namely the key-node-sharing used in the organizing and managing the overlay network is proposed to improve the scalability of OFM. The OFM can guarantee any two nodes that may be connected directly or indirectly, and the request can be delivered along the overlay network efficiently. The efficiency of the resource discovery service based on the model can be therefore improved greatly.