The modular multilevel DC transformer (MMDCT), as a key equipment in DC grids, performs DC voltage conversion, power transmission, and electrical isolation. Its stable operation requires effective voltage balancing control of numerous cascaded submodules. Existing methods struggle to reliably achieve capacitor voltage balancing of submodules under wide voltage gain and full power range. To address this, a control method is proposed for capacitor voltage balancing of submodules within an MMDCT arm. In this method, the quasi two-level modulation is realized by changing the duty cycle of the driving pulse for each submodule. Based on these varying duty cycles, unequal charging control of submodule capacitors is carried out, and the duty cycles are determined according to the sorted capacitor voltages, thereby enabling voltage balancing among the submodules. The proposed method enables MMDCT to operate under a wide voltage gain and full power range, without requiring real-time detection of arm current and with low computational complexity. Finally, simulations and experimental results validate the theoretical analysis and confirm the feasibility and effectiveness of the proposed voltage balancing method.