Ad-hoc mobile wireless network is an infrastructureless network with no fixed routers and hosts. Quickly changed topology, limited bandwidth and limited energy are the main characteristics of these networks. In ad-hoc mobile networks some links may be unidirectional due to the hidden terminal problem. Traditional protocols are not well suited for the mobile environment due to the considerable overhead produced by periodic route update messages and their slow convergence to topological changes. In this paper, we proposed an on-demand routing protocol UAOR for ad-hoc mobile networks with unidirectional links. The major goal of on-demand is to minimize control traffic. UAOR consists of route discovery and route reconstruction phases. In route discovery, the nodes select routes depending on the affinity, which is inspired by ABR and the shortest path. Every node broadcasts hello message every t seconds so that the downstream neighboring nodes can count the affinity. If the forwarding node has route to the destination, it appends route to the route request message and sends it to the destination without broadcasting. When the destination receives the route request, if in the destination's routing table there is a route to the source, the destination sends route reply to source directly by this route. Otherwise, the destination sends reply back to source similarly as the route request. When the source node obtains the route, it uses source route to send packet. We use hello message to achieve route reconstruction. When a link is broken (the downstream neighboring node dose not receive the hello message for T seconds), the downstream nodes carry the broken link in their hello message for only a T seconds. All nodes that received this hello message will rebroadcast broken links in their hello message for T seconds until to the source node. Every node broadcasts a broken link for noly T seconds, then deletes it from hello message, which reduces the overheads of route reconstruction and ensures the source node know the failure of the route including the broken links. When a node or a group of nodes leave the network, their route table would update to avoid the failure routes. In this paper, we also proved the correction of UAOR and analyzed the time and communication overheads of route reconstruction. We compared UAOR with UAHR and NUDL and found that UAOR has better performance than these two protocols.