Many routing protocols have been proposed for mobile ad hoc networks. Among these protocols, the on-demand routing protocols are very attractive because they have low routing overhead. However, few of the existing on-demand routing protocols have considered the link heterogeneity, such as the different communication rate, different Packet Error Ratio (PER). As a result, the routes tend to have the shortest hop count and contain weak links, which usually provide low performance and are susceptible to breaks in the presence of mobility. In this paper, we analyze the existing on-demand routing protocols and propose a Link Heterogeneity Aware On-demand Routing (LHAOR) protocol, where the link quality and mobility are considered. Specifically, the Local Update (LU) is proposed and the link metric is inversely related with the Received Signal Strength Indicator (RSSI). By using the LU method and RSSI information, the routes adapt to the topology variation and link quality changes, and reach the local optimum quickly, which contains strong links and has a small metric. Simulation and experiment results show that our LHAOR protocol achieves much higher performance than the classical on-demand routing protocols.