The modular multilevel dc-dc converter emerges as a promising solution for the medium-voltage (MV) dc system due to its galvanic isolation, voltage conversion, and bidirectional power transmission capabilities. However, different from the traditional dc-dc converter, both the circulating energy and transmission power must be precisely controlled to achieve high dynamic and steady-state performance. In this article, the average value and small-signal models are developed for the series-arm modular multilevel dc-dc converter (SAMMDC) with quasi-square-wave modulation and phase-shifted control. A novel MV terminal current feedforward (MCFF) control strategy is proposed. First, the average value and small-signal models of the SAMMDC, which can describe the low-inertia circulating current characteristic of the modular multilevel structure, are rigorously derived utilizing the reduced-order method and the differential- and common-mode principles. Subsequently, the equivalent open-loop transfer function of the SAMMDC with dual-loop control is established, facilitating frequency analysis. Furthermore, the implementation of the proposed MCFF control strategy and design considerations are presented to increase crossover frequency for improved dynamic performance. Finally, experimental validation of the theoretical analysis and the control strategy is provided through results obtained from a 3.2-kW SAMMDC prototype.