In this paper, an optimized model predictive control (MPC) method with fixed switching frequency (FSF) is proposed to eliminate the common-mode voltage (CMV) and balance the capacitor voltage. Firstly, the zero CMV vector diagram is divided by finite control set MPC (FCS-MPC) to obtain the candidate vectors effectively. Then, in order to control the capacitor voltage and avoid the great computational burden originated from the redundant switching combinations, a piecewise control scheme is proposed to determine the required ones directly. The sequence generated by the selected vectors is further optimized for the purpose of saving switching transitions according to the internal and external parts of the vector diagram. Finally, the duty ratios are evaluated based on the results of the FCS-MPC in dividing sectors so as to avoid any extra complex calculation. The experimental evaluation has been carried out to validate the feasibility and effectiveness of the proposed method.