Focusing on load characteristics of inverted plasma cutting power supply, this paper puts forward a nonlinear control method. This method integrates fuzzy control technology into the controller of power supply, thereby optimizing dynamic characteristics of power supply. The SIMULINK simulation technology is also used. To compare steady-state precision, robustness, response speed and other control indexes between fuzzy control and conventional PI control, the comparative simulation experiments were made respectively under constant non-disturbance steady-state condition, aperiodic load disturbance condition, and periodic load disturbance condition. The simulation results show that power supply with fuzzy controller has perfect steady robustness, fast system response and strong harmonic suppression ability. The simulation model is accurate and reliable, and it can be an efficient tool for further studying mechanism and algorithm optimization of plasma cutting power supply.