Abstract: Wireless mesh network is a new type of broadband wireless network structure, which combines the advantages of wireless local area network and ad-hoc network. The research on wireless mesh network is one of the emerging research focuses about wireless networks. Based on the logic of events, the substitution rule is proposed to ensure the equivalent conversion of user interaction information in the process of property substitution by combining event structures, event classes, axiom clusters and random number lemma. With the basic sequences of authentication protocol between client and LTCA constructed by logic of events, the protocol actions between client and LTCA are formally described, and strong authentication property of the protocol is proved. Under reasonable assumptions, the security property of the authentication protocol between WMN client and LTCA is verified, and the research shows that both the security attributes of wireless network protocols and the authentication property between different principals of cryptographic protocols can be proved by logic of events. By simplifying the formal proof steps with flow chart, the process of logic of events proving protocol’s security property is described, similarly, by comparing and analyzing logic of events with other logical reasoning methods, the universal applicability of logic of events is shown.