This paper presents an averaged model and a small-signal model of a bidirectional dual active bridge (DAB) DC-DC converter. Based on the proposed model, the stability and transient power flow in the system can be analyzed. A novel hybrid controller is proposed for the phase-shift based feed-back and feed-forward control of a 600V/10kW prototype. The hybrid controller can ease the difficulties of the parameter selection of a traditional PI. The effectiveness of the models and proposed hybrid controller are validated by simulations and experiments in both transient and steady state operations.