This paper proposes a new on-demand redundant-path routing protocol considering time synchronization based path redundancy as one of route selection criteria. Path redundancy implies how many possible redundant paths may exist on a route to be built up. Our proposal aims to establish a route that contains more redundant paths toward the destination by involving intermediate nodes with relatively mode adjacent nodes in a possible route. Our approach can localize the effects of route failures, and reduce control traffic overhead and route reconfiguration time by enhancing the reachability to the destination node without source-initiated route re-discoveries at route failures. We have evaluated the performance of our routing scheme through a series of simulations using the Network Simulator 2 (ns-2).