With dc short circuit fault ride through capabilities, full-bridge submodule (FBSM) based modular multilevel converter (FB-MMC) has gained much interest as the FBSM capacitance can be reduced significantly when the modulation index equals 1.414. In this paper, the analytic expression of the injected circulating current, which minimizes the FBSM voltage ripple of the FB-MMC, is derived. Based on these derivations, the impact of zero sequence voltage injection (ZSVI) on the injected circulating current is analyzed in detail. It is shown that, with ZSVI, the amplitude of the injected circulating current can be reduced about 14% for achieving FBSM voltage ripple minimization, which has benefits to decrease the current stress of the semiconductor devices. Finally, the correctness of the presented analysis is verified by comparative simulation results on a ±200 kV/600 MW FB-MMC system.