The composite nonlinear feedback control technique is developed for a class of linear systems with actuator saturation, which consists of a linear and a nonlinear feedback parts without any switching element. The linear part is to yield a quick response in face of the actuator limits for the desired input levels. The nonlinear part is to reduce the overshoot caused by the linear part as the system output approaches the target. It is shown that the technique is capable of beating the time-optimal control in asymptotic tracking situations and can be applied to design servo systems that deal with “point-and-shoot” fast targeting.