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. Index Terms-Modular multilevel converter, compact volume, high step-ratio, dc grids. NOMENCLATURE Ch Control headroom D Duty-cycle of the near-square-wave ES Sum of the energy stored in all capacitors ETs, EBs Energy stored in the top stack and bottom stack fo, fs Operation frequency, switching frequency fr SM sorting and selection frequency iBac AC component of the bottom stack current Manuscript