In this article, a model predictive control (MPC) with common-mode voltage (CMV) suppression is proposed for single-phase cascaded H-bridge (CHB) inverters, which can also simultaneously achieve control objectives of grid-connected current tracking, voltages balancing of different H-bridge submodules on the DC-side and switching frequency reduction. To suppress high-frequency components of the common-mode voltage without additional switching devices, the algorithm proposed designs the predicted and reference values of the CMV and incorporates them in the cost function. At the same time, the capacitor voltages balancing control is integrated in the calculation of the optimal modulation function of the H-bridge, which reduces the complexity of control effectively. Besides, switching times of the MOSFETs are compared in two cycles. The cost function is constructed to represent comprehensive effect of the control. Finally, an experiment is performed on the hardware-in-the-loop experimental platform. The experimental results show that the proposed algorithm can offer a better voltage THD and reduce the times of switch action by nearly half while maintaining high-precision current tracking and maximum power point of photovoltaic modules, which alleviate the potential electromagnetic interference and cabling problem.