Path following control is a crucial technology for intelligent vehicles, and the control accuracy and the robustness under various road adhesive conditions are two key elements of this technology. However, the accuracy and the robustness are hard to be achieved simultaneously owing to the uncertainties in a vehicle dynamics model, especially the perturbation of tire cornering stiffness. To deal with the uncertainties, a multi-model adaptive method is introduced in this study. Firstly, the basic theory of the method is derived, and the adaptive law of each vertex sub-model to the real model is proposed, with its convergence proved by the Lyapunov theory. Then, a vehicle dynamics model and a vehicle-road combined model are built, and the convex polyhedron including all possible perturbation of tire cornering stiffness is established with multiple sub-models. The adaptive law is derived according to the vehicle dynamics model, and the feedback controller of the sub-model in each vertex is derived by the linear quadratic regulator (LQR) method based on the vehicle-road combined model. Simulation results show that the proposed controller can not only ensure the robustness, but also overcome the conservative problem of previous robust methods, achieving excellent performance under various road conditions. Finally, a rapid prototyping test platform is established for further evaluation. Results show that the proposed algorithm has excellent real-time performance, suggesting an excellent potential of its engineering application.