Flying capacitor multicell (FCM) converter is one of the well-known breeds of multilevel converters. There are several configurations of flying-capacitor-based converters presented and reviewed in the literature. One of the promising topologies of the FCM converter suitable for single/threephase applications requiring isolated converters is H-Bridge (Full-Bridge) FCM converter wherein two FCM converters are connected back-to-back encircling one dc voltage source. Due to a superior line-to-line harmonic performance of the level-shifted-carrier pulse-width-modulation (LSC-PWM), this paper proposes an active voltage control of five-level H-bridge FCM converter operated under LSC-PWMs. The general scheme of the proposed active voltage balancing is implemented by utilization of logic-gates without requiring any lookup table. The five-level H-bridge FCM is simulated in PSCAD and the simulation results are provided. Moreover, the performance of the proposed active voltage balancing is investigated under different LSC-PWM strategies to show which one results in a better harmonic performance and which one results in less voltage ripple across the flying capacitors.