An isolated bidirectional dc-dc converter, which combines parallel-connected two-level converters (TLCs) on the medium-voltage side and a modular multilevel converter (MMC) on the high-voltage side, namely a TLC-MMC converter, is a promising candidate for the interconnection of medium-voltage direct current (MVDC) and HVdc grids. Different from typical phase-shift controlled isolated bidirectional dc-dc converters, transformer currents of a TLC-MMC converter are regulated by the MMC in a closed-loop manner in order to achieve extremely low switching losses and low total device rating of power-semiconductor devices in TLCs. This paper addresses the dedicated operation technique and the voltage-balancing control of the TLC-MMC converter. The MMC in the TLC-MMC converter operates with six-step phase voltages and sinusoidal phase currents. Such an operation makes the MMC present remarkable differences to ac-dc applications. The direct-modulation technique, which is the most-used technique performed to MMCs in line-frequency ac-dc power conversion, has been concluded not applicable to the MMC in a TLC-MMC converter due to the significant sixth-order oscillation resulted in the dc-link voltage. Thus, the indirect-modulation technique is employed, and consequently a closed-loop voltage-balancing control is mandatory for the MMC. Possible measures for voltage balancing have been explored, and effective voltage-balancing control with a simplified implementation is proposed. Validity and effectiveness of the proposed control strategy have been verified by both simulations and experiment using a downscale prototype.