This paper suggests a suboptimal control scheme of an active suspension system with an asymmetric hydraulic cylinder. In this paper a quarter car model including a nonlinear actuator dynamics is used. A feedback linearization technique is applied to obtain a linear model. An LQ regulator is designed with the linear model to keep robustness against sprung mass variation. The gain of the LQ regulator which depends on the damping coefficient of the damper is calculated by using an RBF neural network for real time application. The improvement achieved with our design is illustrated through comparative simulations.