The disadvantages of the conventional model predictive current control method for the grid-connected converter (GCC) with an inductance-capacitance-inductance (LCL) filter are a large amount of calculation and poor parameter robustness. Once parameters of the model are mismatched, the control accuracy of model predictive control (MPC) will be reduced, which will seriously affect the power quality of the GCC. The article intuitively analyzes the sensitivity of parameter mismatch on the current predictive control of the conventional LCL-filtered GCC. In order to solve these issues, a model-free predictive current control (MFPCC) method for the LCL-filtered GCC is proposed in this paper. The contribution of this work is that a novel current predictive robust controller for the LCL-filtered GCC is designed based on the principle of the ultra-local model of a single input single output system. The proposed control method does not require using any model parameters in the controller, which can effectively suppress the disturbances of the uncertain parameter variations. Compared with conventional MPC, the proposed MFPCC has smaller current total harmonic distortion (THD). When the filter parameters are mismatched, the control error of the proposed method is smaller. Finally, a comparative experimental study is carried out on the platform of Typhoon and PE-Expert4 to verify the superiority and effectiveness of the proposed MFPCC method for the LCL-filtered GCC.