Dual active bridge (DAB) DC-DC converter is widely used in DC micro-grid and electric vehicle charging field. It has advantages of high-power density, easy implementation of soft switching, and bi-directional power transmission capability. Traditional linear controllers have difficulty in meeting the increasing requirements for speed and robustness. In this paper, a novel Brayton-Moser based passivity control strategy is proposed to improve the control strategy of a DAB DC-DC converter. For increase the robustness of the control to parameter variations, the Brayton-Moser is combined with passivity theory in this paper. Further, the Brayton-Moser based controller of DAB was designed based on the Brayton-Moser model. Finally, the simulation based on MATLAB is built to validated.