The modular multilevel converter−bidirectional DC−DC converter (MMC−BDC) has been proposed to be utilized in the vessel integrated power system to interconnect the medium voltage bus and the distributed energy storage elements. In the shipboard applications, MMC−BDC faces unbalanced sub-module power operation because of the inconsistent state-of-charge (SOC) of the energy storage elements. Researchers have investigated into the unbalanced operation principle of MMC−BDC and proposed some unbalanced operation control strategies, but these traditional strategies do not perform well in both aspects of operating range and efficiency. Therefore, this paper proposes a novel Lyapunov-function-based feedback linearization control strategy for the independent sub-module voltage control of MMC−BDC, which not only shows wide unbalanced operation range and high efficiency, but also realizes the decoupling and symmetrical control of the sub-module capacitor voltages.