The nonlinear mathematical model of electric vehicle steering system based on magnetic gear composite motor is established. The multi-cycle, quasi-period and chaotic motion appear under certain parameters and operating conditions in the steering process of steering system. The maximum Lyapunov exponent graph and points are obtained. The chaotic numerical simulation analysis of the established steering system model is carried out. Then the complementary sliding mode control design is adopted, and the adaptive diagonal recursive cerebellar model controller is used to improve the system performance, effectively suppress the chaos in the lateral motion of the vehicle, and improve the safety and stability of the steering system during the driving of the electric vehicle. This control strategy is effective.