This paper provides a detailed analysis on the threats of topology-exposure in Mobile Ad Hoc Network (MANET) and proposes a secure topology-hiding multipath routing protocol based on the analysis. In Route Discovery, the new protocol exposes no routing information in packets to hide the network topology and adopts a node-excluded mechanism to find multiple paths. During this process, this protocol implements on-demand Neighbor Discovery to verify node identities. In Route Maintenance, a fault detection mechanism is designed to provide assurance that the selected paths are available and secure. Considering the factors of both reaction time and the path length, the scheme aims to find the shortest secure path. The security analysis shows that this scheme can resist the black hole attack, the wormhole attack, the rushing attack, the sybil attack, and other types of common attacks. Through extensive simulations, results demonstrate that this approach can find many more active paths than SRP without bringing negative influences into the normal scenario. Furthermore, this solution largely improves the packet delivery ratio in the black hole attack scenario at an acceptable cost.