The paper presents a new disturbance rejection version of the Smith predictor control system (Smith 1959) and of the multivariable one (Donoghue 1977). The method uses a dynamical compensator and can decay the output error to disturbances as fast as desired without any change of the input-output transfer characteristics of the Smith predictor control system. The design procedure of the compensator and the mechanism of the disturbance rejection are discussed. Numerical examples are given to demonstrate the availability of the method.