The Dual Active Bridge (DAB) DC-DC converter is popular for its advantage of high power density, zero-voltage switching (ZVS) and bidirectional power flow capability. It is important to improve the power density and efficiency of DAB converter. With the development of wide band-gap semiconductor device, such as GaN HEMT, the efficiency and power density of DAB converter can be improved significantly by taking advantages of GaN HEMT superior performance. In this paper, a DAB converter design based on GaN HEMT device is presented. The system design and design consideration of DAB converter is discussed in detail, and the optimal design of high frequency transformer is introduced. Moreover, the gate driver circuits and power circuits are designed carefully to minimize the parasitic inductances. Therefore, we provide a useful reference for the practical application of DAB circuit. Finally, a prototype of 400 W DAB is built in laboratory. The power density is calculated as 39 W/inch³ and the peak efficiency is more than 95%.