In this article, an event-triggered adaptive dynamic programming (ADP) method is proposed to solve the robust control problem of unmatched uncertain systems. First, the robust control problem with unmatched uncertainties is transformed into the optimal control design for an auxiliary system. Subsequently, to reduce controller executions and save computational and communication resources, an event-triggering mechanism is introduced. By using a critic neural network (NN) to approximate the value function, novel concurrent learning is developed to learn NN weights, which avoids the requirement of an initial admissible control and the persistence of excitation condition. Moreover, it is proven that the developed event-triggered ADP controller guarantees the robustness of the uncertain system and the uniform ultimate boundedness of the NN weight estimation error. Finally, by using the F-16 aircraft and the inverted pendulum with unmatched uncertainties as examples, the simulation results show the effectiveness of the developed event-triggered ADP method.