In this paper, the model-matching control in the longitudinal autonomous driving system is investigated by vehicle dynamics simulation, which contains nonlinear subcomponents and simplified subcomponents. The design of the robust model-matching controller is performed by the characteristics of the 2 degrees of freedom controller, which is composed of the feedforward compensator and the feedback compensator. It makes the characteristics of tractive and brake force to be equivalent to the specific transfer function, which is suggested as the reference model. Mathematical models of vehicle dynamic analysis including the model-matching control are constructed for computer simulation. Then, simple examples on open-loop simulation without any controller and closed loop simulation with the model-matching controller are applied to check the validity of the robust controller. As the practical example, the autonomous driving system in the longitudinal direction is adopted. It is proved that the model-matching control is effective and adequate to the disturbances and the perturbations, which are shown in the responses of the change of a vehicle mass and a road gradient.