Dual-active-bridge (DAB) enabled dc microgrids stabilization is investigated in this article. DAB has two control objectives: load current regulation and the dc-bus voltage stabilization. In multiobjective control applications, the conventional proportional integrator (PI)-based controllers face challenges in the control loop coordination. The saturation of the loops largely deteriorate the control performance. Moreover, the system impedance has to be measured before designing the active damping control. In this article, a moving discretized control set - model predictive control (MDCS-MPC) is proposed for DAB. The proposed MDCS-MPC is inherently a good choice for multiobjective control. It provides several advantages, such as a good tradeoff between two control objectives and adaptive performance on system impedance. The evaluation and comparison of the proposed MDCS-MPC and PI are carried out. Experiments on a 270-270V, 20 kHz, 1 kW DAB converter are conducted to verify the theoretical claims.