In this paper, we developed an efficient global on-demand routing protocol for mobile ad hoc networks. In this protocol, nodes do not update their routing tables immediately if they change status, such as movement, addition or deletion. Instead, nodes dynamically run the Dijkstra?s algorithm on-demand to keep the shortest paths for packet transmissions efficiently. Our protocol is called as "global on-demand" because the on-demand feature covers the whole (global) network. With these critical features, our protocol has higher packet delivery rate and lower end-to-end delay than table-driven protocols. Moreover, our protocol shows low routing load as in the local on-demand protocols, and improves the sub-optimal hierarchical routing and memory consuming problems as in the existing hybrid protocols.