In order to improve the robustness of the sliding mode control algorithm of the four-phase interleaved parallel Buck converter, an improved adaptive non-singular terminal sliding mode PI (ANTSMC-PI) dual closed-loop control strategy based on linearly expanding state observer (LESO) is proposed in this paper. First, two LESO observers are designed to estimate the matched and mismatched disturbance in the system dynamic model, respectively. Second, the estimates of the observers are Integrationed into the outer-loop controller, and an improved sliding-mode controller is proposed to achieve error-free tracking of the output voltage to the reference voltage; while the PI controller is used for the current inner loop to ensure the equal current flow in each phase of the system. Finally, the stability of the designed controller is demonstrated by using the lyapunov stability principle. The simulation in Matlab/Simulink platform shows that the proposed scheme can effectively reduce the output ripple and improve the system dynamic performance compared with the traditional non-singular terminal sliding-mode PI control strategy.