The inverted plasma cutting power supply has multi-variable, nonlinear, strong coupling and time-varying characteristics and technological requirements. This paper proposes a decoupling control strategy based on fuzzy neural network expert system for the multi-parameter dynamic coupling and the uncertainty of the optimal output of the cutting process. It achieves the reasoning and decision-making through the fuzzy production rules. It adjusts the parameters of the neural network by adaptive algorithm, thus gets the optimal reference current of closed-loop controller, and then achieves the given current closed-loop control by means of RBF neural network adaptive PID controller. The simulation results show that the controller has good self-adaption and approximation. Compared with traditional PID controller, the system has great improvement on static accuracy, robustness and response speed. It is verified that the controller has the advantage of dealing with discrete problem and coupling multivariable problem.