Various driving support systems to avoid traffic accident have developed and have been put in the real world. On the other hand, only a few collision avoidance systems with the steering wheel have been put in the real world. In addition, most of these systems target avoiding other vehicle. But the number of traffic accidents concerned with a bicycle is next to it of a vehicle. So driving support system for collision avoidance of the bicycle is necessary. In this paper, steer-by-wire is introduced into the steering wheel of the vehicle and the driving support system which realizes the most suitable steerage to avoid collision with the bicycle by considering position, velocity, and inclination of running bicycle is proposed. First, the modeling of the driving support system is introduced. Second, the control system is designed which is composed of impedance control and model predictive control. Third, the driving simulation is conducted to verify the effect of the proposed method. Finally, conclusion and the future works are described.