Experimental advanced superconducting tokamak (EAST) fast control power supply (FCPS) is an essential device to realize balance control of plasma vertical displacement during controllable nuclear fusion process. The primary control purpose of EAST FCPS is to quickly output current to track reference current. Change of load inductance parameters due to plasma motion poses higher robustness requirements for fast tracking control of output current. Therefore, an improved gray prediction parameter identification sliding mode control method is proposed to achieve fast tracking and robust control of output current under changes in load inductance parameters. Parameter identification sliding mode control method applied to identify load inductance parameters in real‐time, accurate EAST FCPS output current tracking sliding mode control model is established. High‐order terms are added to discrete exponential convergence reaching law, and a new smooth saturation function is designed to replace traditional sign function to achieve chattering suppression and accelerate system convergence speed. Gray prediction used in current sampling to achieve output current trajectory advanced prediction to further accelerate output current response speed. Four times equal interval time sampling within a fixed switching period and new information priority period by period prediction is proposed to improving gray prediction, achieving digital control delay compensation, and improving prediction accuracy of output current trajectory at abrupt edge. Simulation and experimental verification show that the proposed improved gray prediction parameter identification sliding mode control method has good output current tracking control performance under changes in load parameters. Compared with PI control method currently used in engineering, the proposed control method performs better in output current fast response and overshoot suppression.