A system identification method—voltage mapping method for a single degree of freedom electromagnetic vibration energy collector is proposed. The method can accurately identify the recovery force function with strong nonlinearity，electromagnetic electromechanical coupling function and equivalent inductance function even if the specific forms of these functions are unknown.Two typical nonlinear model examples are proposed to verify，one is an electromagnetic vibration energy collector system with nonlinear elastic recovery force（the electrical equation part is linear），and the other is a complex electromagnetic vibration energy acquisition system with nonlinear elastic recovery force and nonlinear electrical equations. Runge-Kutta method is used to obtain the time history response of the above two examples under the excitation of simple harmonic vibration，and the identification method proposed above is used to obtain the nonlinear elastic resilience，damping resilience，electromagnetic force and inductance voltage of the system. Therefore the corresponding nonlinear stiffness function，damping function and electromagnetic electromechanical coupling function and equivalent inductance function can be identified successfully. The results show that the identification results are in good consistency with the accurate results，and the method proposed in this paper is verified to be effective and accurate.