In near-field energy transmission, it has been proved that magnetic coupling wireless power transfer (MC-WPT) is a promising energy transmission method. Traditionally, the MC-WPT system is established based on a linear resonant circuit. Recently, it has been reported that nonlinear MC-WPT system shows more advantages. However, nonlinear characteristics of the nonlinear MC-WPT system are not fully recovered. In this paper, a nonlinear MC-WPT system which can be described by Duffing equation is presented. The mathematical model of the equivalent circuit is developed. The related nonlinear characteristics under the impact of driving force are investigated. It is found that the driving force has a direct impact on the system performance. The operation of the nonlinear MC-WPT system varies from periodic sinusoidal state to periodic non-sinusoidal state even to chaotic state when the driving force increases. It should be mentioned that the chaotic state should be avoided. Generally, the MC-WPT system should be operated in periodic sinusoidal state which only covers a small range of driving force. For the system operated in periodic non-sinusoidal state, a waveform correcting circuit is designed. The simulated and experimental results show that the restriction of the driving force on the operation of the system is eliminated with a waveform correcting circuit added. It is possible for the nonlinear MC-WPT system to be operated in a much wider range.