This paper presents a current model predictive control (CMPC) method for two-level grid-connected converters. As known, model predictive control (MPC) strategy is a model-based control method. However, the temperature rise and current change will lead to the change of the inductors, resistance of the circuit. Thus, when the parameter in the prediction model is inconsistent with the one in actual circuit, the current accuracy of the conventional CMPC method will be reduced obviously. So, in this paper, to improve the parameter robustness of the CMPC method and improve the grid-connected quality further. A new weighted CMPC strategy is creatively proposed. Through detailed theoretical analysis, the principle of the proposed method to reduce the influence of parameter errors is revealed. Finally, the effectiveness and feasibility of the proposed method are verified by simulation.