The disadvantages of the conventional model predictive current control method for a three-phase LCL grid-connected inverter are the need for much calculation and poor parameter robustness. To help eliminate these issues, a nonparametric sliding mode predictive current control method for a three-phase LCL grid-connected inverter is proposed. This method uses the sliding mode control theory to establish a novel nonparametric current control cost function. This can realize grid current predictive control without using model parameters, and simplify the prediction process of the control system. Also, this method eliminates the inverter side current and capacitor voltage sensors, saves hardware cost and improves the operational reliability of the system. Finally, from the advantages of conventional model predictive current control and sliding mode predictive current control, an adaptive predictive control method for a three-phase grid-connected inverter is proposed to improve the adaptability of grid-connected inverter control with model parameter inaccuracy. The experimental results show that the proposed control strategy has less grid current control error when the system parameters are inaccurate, and the robustness of system parameters is effectively improved. This work is supported by the National Natural Science Foundation of China (No. 51907046 and No. U2004166).