With the development of the advanced driver assistance system and autonomous vehicle techniques, a precise description of the driver’s steering behavior with mathematical models has attracted a great attention. However, the driver’s steering maneuver demonstrates the stochastic characteristic due to a series of complex and uncertain factors, such as the weather, road, and driver’s physiological and psychological limits, generating negative effects on the performance of the vehicle or the driver assistance system. Hence, this paper explores the stochastic characteristic of driver’s steering behavior and a novel steering controller considering this stochastic characteristic is proposed based on stochastic model predictive control (SMPC). Firstly, a search algorithm is derived to describe the driver’s road preview behavior. Then, the internal vehicle model including driver’s knowledge of the vehicle lateral dynamics is derived by a nonlinear 2-DOF model, and a sideslip angle perception model is proposed in the state feedback process to describe the stochastic characteristic of driver’s steering behavior, which is characterized by a gauss stochastic variable, whose mean represents the real sideslip angle and variance is associated with driver’s steering skills and vehicle lateral dynamics. Moreover, the steering control rule is formulated to generate the trajectory track steering commands according to the trajectory error and steering input. Finally, the proposed SMPC driver model is validated. The results demonstrate the SMPC driver model has an excellent trajectory track capability and describes the stochastic characteristic of driver’s steering behavior precisely.