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In highly mobile Ad hoc networks, network topology changes frequently, and routes have a poor stability, which degrades communication performance. This paper proposes a multipath routing protocol LBR (Link lifetime based Backup Routing) to improve routing stability. LBR is based on link lifetime, while obtaining the shortest path between source and destination through flooding, and setting up a local backup path for each link in the primary path concerning link lifetime. This scheme effectively avoids backup paths being out-of-date and increases the availability of backup paths. Both theoretical analyses and simulation results show that LBR has an improvement in route lifetime, packet delivery ratio, end-to-end delay, and so on, compared with single-path routing protocols.