Pulsed power loads (PPLs) are becoming prevalent in medium-voltage naval dc micro-grids. To alleviate their effects on the system, energy storages are commonly installed. For optimal performance, their interface converters need to have fast dynamics and excellent disturbance rejection capability. Moreover, these converters often need to have voltage transformation and galvanic isolation capability since common energy storage technologies such as batteries and supercaps are typically assembled with low-voltage strings. In order to address these issues, a moving discretized control set model predictive control (MDCS-MPC) is proposed in this paper and applied on a dual-active-bridge converter. Fixed switching frequency is maintained, enabling easy passive components design. The proposed MDCS-MPC has a reduced prediction horizon, which allows low computational burden. The operating principle of the MDCS-MPC is introduced in the development of a cost function, which provides stiff voltage regulation. Resonance damping and sampling noise resistance can also be achieved with the proposed cost function. An adaptive step is introduced to enable a fast transition. Assessments on the performance of the proposed MDCS-MPC are conducted. Comparisons with other control methods are also provided. Experimental validations on a 300 V/300 V 20-kHz 1-kW dual-active-bridge converter are carried out to verify the theoretical claims.