Traditional model predictive current control has been widely studied in the field of grid-connected inverter control due to its rapid response and multi-objective optimization capabilities. A data driven model-free predictive current control strategy is proposed to address the problem of control performance degradation caused by parameter mismatch in traditional model predictive current control. Firstly, the weighted average current method is used to reduce the order of the third-order LCL filter system, suppressing oscillations caused by LCL resonant frequency. Then, the ultra local model is adopted to simplify the traditional predictive current model, and a linear extended state observer is designed to estimate and compensate for system disturbances, thereby improving the accuracy of current prediction. Finally, the recursive least squares method is used to update the system model online based on system operating data, reducing the dependence of the control system on parameters. The simulation and hardware-in-the-loop experimental results demonstrate that compared to traditional model predictive current control, the proposed control strategy exhibits strong robustness and good steady-state performance under parameter mismatch conditions.