Summary: Driver's lateral control on curved roads plays a significant role in reducing or avoiding the crashes. To understand and predict driver performance on curved roads, a computational model was developed in a cognitive architecture, the Queueing Network-Model Human Processor (QN-MHP), with the integration of vehicle dynamics principles (i.e., how to steer based on near and far angles) and the reference trajectory tracking method (i.e., how to steer on the road varying with radius of road curvature). The model was implemented with four major components: road information, vehicle dynamics, visual perception, and cognition & motor controls. The model outputs were validated with the corresponding human subject performance in the literature. The performance results of the model highly fitted the human subject data such as steering wheel angle.