This paper presents a simple and innovative Capacitor Voltage Balancing (CVB) strategy for Modular Multilevel Converters (MMC) based on full H-bridge cell topologies. The method computes specific modulation indexes for each cell using the explicit solution of an underlying optimal control problem. Based on the structure of its analytical solution, the proposed CVB scheme is integrated to a Phase-Shifted PWM scheme with an easy implementation. Experimental results obtained from a nine-cell single-phase converter demonstrate an improved performance of the proposed method, especially under transient operating conditions.