Aiming at improving the quality of output current when the inverter is connected to the grid, this paper proposes a control strategy of neutral point clamped (NPC) grid-connected inverter based on radial basis function neural network (RBFNN) multi-step predictive control. Firstly, the predictive control model for output current of NPC inverter is constructed by αβ coordinate transformation. Then the future values of output current are predicted for each voltage vectors, using the RBFNN prediction model. After the predicted values are obtained, a cost function f is calculated for each voltage vectors and the optimal voltage vector which minimizes cost function is selected. The switch state corresponding to the optimal voltage vector is applied to the inverter in the next sampling period. Thereby the control of grid-connected output current can be achieved. The simulation results show that the RBFNN multi-step predictive control method improves the capability of current tracking and reduces the harmonic rate of output current. The proposed method can balance output current under the condition of grid voltage imbalance. INDEX TERMS Inverter, RBF neural network, predictive control, optimal voltage vector, three-phase current balance.