In multi-terminal dc networks or future dc grids, there is an important role for high step-ratio dc-dc conversion to interface a high voltage network to lower voltage infeeds or offtakes. The efficiency and controllability of dc-dc conversion will be expected to be similar to modular multi-level ac-dc converters. This paper presents a modular multilevel dc-dc converter with a high step-ratio for medium voltage and high voltage applications. Its topology on high-voltage side is derived from the half-bridge single-phase inverter with stacks of sub-modules replacing each of the switch positions. A near-square-wave current operation is proposed which achieves near-constant instantaneous power for single-phase conversion, leading to reduced stack capacitor and filter volume and also increased the power device utilization. A controller for energy balancing and current tracking is designed. The soft-switching operation on the low-voltage side is demonstrated. The high step-ratio is accomplished by combination of inherent half-bridge ratio, sub-module stack modulation and transformer turns-ratio, which also offers flexibility to satisfy wide-range conversion requirement. The theoretical analysis of this converter is verified by simulation of a full-scale 40MW, 200 kV converter with 146 sub-modules and also through experimental testing of a down-scaled prototype at 4.5 kW, 1.5 kV with 18 sub-modules.