In this paper, an adaptive neural asymptotic tracking control scheme with the event-triggered mechanism is presented for a quarter-car active suspension system (ASS) with unknown road inputs and input saturation. In the control design, an auxiliary system is constructed to compensate for the input saturation of the actuator, and a linear filter is introduced to solve the chattering problem of the suspension system under the zero dynamics. By integrating integral-bounded functions into the adaptive law and control law, asymptotic convergence of the tracking error is achieved with high precision. Using the adaptive backstepping control method and introducing the command filter, an event-triggered adaptive neural asymptotic tracking control algorithm is developed, in which the radial basis function neural networks (RBFNNs) are used to approximate the unknown model dynamics. Considering the waste of communication resources in the controller, the event-triggered control (ETC) law in the controller-to-actuator channel is designed. Benefiting from the minimal learning parameters (MLP) technique, the proposed scheme requires updating only one parameter, which reduces computational complexity and saves communication resources. By using the Lyapunov’s method and the Barbalat’s lemma, the asymptotic stability of the closed-loop system is proved, and the constraint conditions for vehicle ride comfort are also guaranteed. Finally, the effectiveness of the proposed method is further verified through simulations and experimental results.