To quickly output sufficient current for plasma excitation control, parallel operation of a structure of multiple branches is adopted in the Experimental Advanced Superconducting Tokamak (EAST) fast control power supply. During the process of parallel operation of multiple branches in engineering, a larger inductance current sharing reactor is used to suppress the circulating current for the branches, which reduces the dynamic response speed of the output current and increases economic costs. In order to achieve cost savings and improve the dynamic response speed of the output current, the parallel branch current model of the EAST fast control power supply is analyzed, and the current of each branch is reconstructed into two parts: the current flowing to the load end and the circulating current flowing to other branches. Without changing the circuit structure and increasing the additional complex communication system for each branch, observation of the current flowing to the load end from each branch is achieved. Based on the observed current, a super-twisting sliding mode controller (STSMC) is designed to suppress the circulating current flowing through branches. To realize fast output of the branch current and circulating current suppression for the branches, a new STSMC with a linear term and parameter adaptive structure is designed, speeding up the convergence rate of the whole control system. The linear term and designed parameter adaptive structure based on the sliding mode system status ensure fast convergence speed and excellent control performance of the system. Simulation and experiments show that the designed control method can achieve fast output current control for each branch and that the tracking performance of the total output current is good. While reducing the inductance of the current sharing reactor, the circulating current for the branches is effectively suppressed compared with traditional control methods. The proposed method has great significance in cost savings and performance improvement in engineering practice applications.