A state space model for the neutral point clamped three-level grid-connected inverter is derived in detail，based on which a finite set optimal predictive（FSOP）control method is proposed.The proposed FSOP method is used to select the optimal switching vector from a finite set according to a cost function.The finite set is composed of27switching vectors，and the cost function is composed of the error of output current，the neutral point unbalanced voltage and the switching time of devices.The flow chart of FSOP control is given and the control performance is assessed by simulation and experiment.Experimental results show that the proposed FSOP method has a flexible control purpose，and the synthetic performance of the inverter can be optimized just by adjusting the weighting coefficients of factors in the cost function.FSOP control has bypassed the structure of controller plus modulator in the traditional control method and has a quick response in tracking the output current reference signals and balancing the neutral point voltage.