In order to improve high-speed emergency steering stability of the vehicles equipped with electromagnetic clutch-electronical controlled hydraulic power steering (E-ECHPS), the feedback tracking linear reference model control strategy was proposed based on differential geometry. First of all, the nonlinear dynamics models were established, including vehicle dynamics model, tire model, steering system model and ESC model, and the correctness of the model was verified by road test and bench test. And on this basis, the affine nonlinear system state equations were deduced. Considering the nonlinearity of tires, hydraulic system and ESC, then the differential geometry theory was applied to implement precise linearization of nonlinear system, and the input and output pseudo linear systems were gained. Because the vehicle state is usually stable when vehicle is under the linear operation condition. The linear reference model with steering system under consideration was built. To achieve tracking of ideal vehicle state, the feedback tracking controller was constructed. Finally, the step steering simulation and single lane changing simulation with steering torque as input signal were carried out under controllable and uncontrollable conditions respectively. The results show that feedback tracking control strategy can improve the stability of the vehicle equipped with E-ECHPS under high-speed emergency steering condition. It provides the basis for E-ECHPS control strategy design.