A modular multilevel resonant dc/dc converter (MMRDC) possesses high power and high voltage rating, which is adopted for high step-ratio interconnection in dc grid applications. However, the current stress and reactive power of MMRDC are high with the conventional quasi-square-wave modulation scheme when in a wide voltage range and light load conditions. Hence, this article proposes an optimized asymmetric trapezoidal wave (ATW) modulation scheme that reduces current stress over wide load and voltage ranges by separately modulating the duty cycles of string output voltage rising and falling processes. The time-domain mathematical model of MMRDC with the ATW modulation scheme is established. Then, based on the soft switching characteristic and reactive current analysis, the optimized operating point of MMRDC can be derived while considering low current stress and zero voltage switching constraint of low voltage side full-bridge switches. On this basis, the numerical solutions of optimized control variables are obtained, and a control block diagram is presented for the practical implementation of the optimized ATW modulation scheme. Finally, a 4kW MMRDC prototype is constructed, and the experimental results verify the correctness and effectiveness of the analysis and the optimized ATW modulation scheme.