Driver behavior is considered one of the most important factors in the genesis of dilemma zones and the safety of driver-vehicle-environment systems. An accurate driver behavior model can improve the traffic signal control efficiency and decrease traffic accidents in signalized intersections. This paper uses a mathematical modeling method to study driver behavior in a dilemma zone based on stochastic model predictive control (SMPC), along with considering the dynamic characteristics of human cognition and execution, aiming to provide a feasible solution for modeling driver behavior more accurately and potentially improving the understanding of driver-vehicle-environment systems in dilemma zones. This paper explores the modeling framework of driver behavior, including the perception module, decision-making module, and operation module. The perception module is proposed to stimulate the ability to perceive uncertainty and select attention in the dilemma zone. An SMPC-based driver control modeling method is proposed to stimulate decision-making behavior in the dilemma zone. The operation module is proposed to stimulate the execution ability of the driver. Finally, CarSim, the well-known vehicle dynamics analysis software package, is used to verify the proposed models of this paper. The simulation results show that the SMPC-based driver behavior model can effectively and accurately reflect the vehicle motion and dynamics under driving in the dilemma zone.