In this article, a method that applies event-triggered (ET) mechanism H ∞ control to continuous-time (C-T) nonlinear systems with asymmetric constraints based on dual heuristic dynamic programing (DHP) structure is proposed. At first, we derive ET mechanism from traditional time-triggered and give the Hamilton-Jacobi-Isaacs (HJI) equation. Second, we give the triggering condition and prove the stability of system under ET mechanism. Then, two neural networks (NNs) are introduced, one of which is the critic network, which is designed to approximate the partial derivatives of value function with respect to inputs, and approximate disturbance policy. The other is the action network, which is used to acquire the estimation optimal control policy. Furthermore, we choose a suitable Lyapunov candidate function to prove that the system and NNs weight estimation errors are uniformly ultimately bounded (UUB). Besides, it is important that we prove that Zeno phenomenon can be avoided. Finally, simulation results are shown that the proposed method is feasible.