Simulation-based vehicle system design and development of various active chassis control systems necessitate an enhanced understanding of driver-vehicle systems, in particular improved modeling of driver driving control characteristics. A number of research efforts have been made in developing driver models in the past few decades. However, little effort has been attempted in modeling driver steering control behavior capturing vehicle-road system parameter uncertainties. In this paper, a novel driver steering control model based on stochastic model predictive control (SMPC) is proposed to effectively incorporate the variations in the vehicle-road system parameters. The proposed SMPC-based driver steering control framework consists of three modules, namely perception, decision and execution, where a multi-point driver preview approach is employed. An internal vehicle dynamics model with the parameter uncertainty in road friction coefficient is formulated to represent the driver's knowledge and adaptation about the variations in road conditions. The SMPC method is then used to minimize a cost function that is a weighted combination of lateral path error and ease of driver control. Simulation analysis about the variant parameters and comparison with an MPC-based driver model demonstrate the effectiveness and robustness of the proposed SMPC-based driver steering control model.