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In this article, we investigate a distributed event-triggered fuzzy synchronization control problem of nonlinear multiagent systems (NMASs) with directed jointly connected switching topologies. An improved distributed estimator is designed to generate an estimated leader signal and its high-order derivatives under directed jointly connected switching topologies, which enables the controller design to be implemented by adopting backstepping technology. Then, with the help of fuzzy logic systems (FLSs), a distributed event-triggered fuzzy synchronization control scheme is proposed by introducing an event-triggered mechanism. Theoretical analysis shows that the NMASs with jointly connected directed switching topologies steered by our developed fuzzy synchronization control scheme achieve output synchronization. The simulation results validate the feasibility of the developed approach.