A current loop improved model-free sliding mode control (IMFSMC) method is proposed to address the issues of steady-state power ripple and excessive current harmonics caused by dynamic loads, parameter mismatches, and single-phase short-circuit grounding faults in modular multilevel converters (MMC). Firstly, based on the mathematical model of MMC system, a model compensation hyperlocal model is constructed for parameter mismatch. Secondly, a time-varying gain adaptive sliding mode approach law is proposed to design a current loop sliding mode model-free feedback controller. Simultaneously, a model compensated improved linearly extended state observer (MCILESO) is designed to estimate unknown disturbances in the hyperlocal model and compensate them to the sliding mode feedback controller. The stability of the controller and observer is proved using Lyapunov function and Hurwitz theorem. Finally, based on MATLAB simulation and RTLAB semi physical platform, compared with PI control and traditional model-free sliding mode control, the results show that the proposed method can greatly improve the dynamic and steady-state performance of MMC systems under dynamic loads, parameter mismatches, and single-phase short-circuit grounding. Reduce the model dependency of MMC system, increase system robustness and anti-interference ability.