The Experimental Advanced Superconducting Tokamak (EAST) fast control power supply (FCPS) is an important device for controlling the vertical displacement of plasma during the nuclear fusion power generation process, adopting a multiple H-bridge invertor branch parallel operation structure to output total current. At the beginning of each shot of plasma discharge, FCPS works in open-loop voltage control mode (VCM) or closed-loop current control mode (CCM) determined by the plasma control system to output current for exciting the load coil, to achieve plasma vertical displacement control. VCM has the characteristics of fast dynamic response speed but poor consistency of branch current and insufficient branch current control accuracy and stability because of open-loop control. CCM has the characteristics of high branch current control accuracy but poor dynamic response and robustness because of control delay and control parameters determined based on engineering experience. To achieve fast and robust control, an improved voltage control method (IVCM) is proposed by combining the advantages of VCM and CCM. In the beginning of establishing the output current, FCPS operates in VCM, and rapid establishment of the output current is ensured. After the output current rapidly increases to the critical value, closed-loop current control is added to VCM to ensure the accuracy of output current control. In closed-loop current control, linear super-twisting sliding mode control is designed to achieve fast and robust control, ensuring good consistency and fast dynamic response performance of each branch current. Simulations and experiments verify that the designed IVCM has better compatibility characteristics in output current stability, control accuracy, and consistency of each branch current compared to VCM.