The wind suddenly blown to the side of the car (i.e, cross-wind effect) is considered as one of the major lateral disturbances, which causes the unstable motion of the vehicle and the persistent driving fatigue for the driver who tracks the desired travel path. In particular, a commercial vehicle having a large side area is greatly affected by this effect. Therefore, many related automotive/car manufacturers still wish to equip their Advanced Driving Assistant System (ADAS) with the crosswind disturbance compensation control system. Meanwhile, in recent advanced vehicle systems, a rack-type motor-driven power steering (R-MDPS) system is more widely used than a column-type MDPS (C-MDPS) due to the structure advantage and the effective steering assistance. Recognizing those two issues, this paper investigates a novel anti-control and estimation strategy of crosswind disturbance for the R-MDPS system of vehicles with non-negligible side surfaces. Specifically, an adaptive disturbance observer (D.O.B) has been proposed to estimate the crosswind effect. Furthermore, using optimal control theory, the compensation control system is designed to assist the driver in two possible situations. One is for when the driver continues to steer the vehicle under the effect of the crosswind, and the other is for when the driver temporarily loses steering control due to the effect. In addition, the control mode selection conditions between two controls are clearly presented to maximize the efficiency and performance of the proposed control system. Finally, the effectiveness of the proposed control system has been evaluated based on the Simulink/Carsim Co-simulation and HILS environments.