Vehicle run-off-road is one of the most frequent and fatal traffic accidents in the United States. Various lane-keeping assistance (LKA) systems have been developed in the last decade to help drivers stay on the road. Most of them are built upon linear driver–vehicle–road (DVR) models and treat road curvature as a disturbance. Albeit effective, their control performance would degrade if road curvature varies rapidly. This paper proposes a novel nonlinear DVR model by integrating a driver steering model into vehicle–road kinematics, which explicitly considers road curvature. Particularly, this nonlinear DVR system has been proven to be differentially flat, and a flatness-based LKA system is designed. Additionally, Model-Free Control is introduced to compensate for system modeling errors. Hardware-in-the-loop simulations and diver-in-the-loop experiments validate the proposed control framework and demonstrate the performance enhancement with respect to a representative linear robust LKA system.