This paper proposes an efficient, secure and anonymous routing protocol based on Weil pairing for wireless mesh networks (WMNs). The proposed protocol considers symmetric and asymmetric links during wireless communication in WMNs. A WMN integrates several types of wireless devices, and induces the asymmetric links that result from different transmission ranges of wireless devices. Enhancing the security and privacy of WMNs has been an important research focus in recent years. Most research on this topic has focused on providing security and anonymity for routing and data in symmetric links. However, the asymmetric links in these protocols have not been addressed. This paper proposes a novel distributed routing protocol suitable for WMNs that include symmetric and asymmetric links. The proposed protocol guarantees security, anonymity and high reliability in WMNs. The proposed protocol generates routes that are shorter than those of previous studies. The proposed scheme protects the real identities of the source and intermediate users, which remain unknown even to the mesh router, while still providing node authentication. Using the proposed protocol, mesh clients anonymously discover a secure route to the mesh router. This protocol also ensures data transmission anonymity and enhances WMN coverage, in addition to assuring security and anonymity.