High-power DC-DC converter will be one of the essential technologies for the future DC grids. Especially, a three-phase dual-active bridge DC-DC (3DAB) Converter is highly suitable for high-power DC systems. Key component within this converter is the high power transformer operated at a medium frequency (MF) range. The design and optimization of this key component is presented in this paper. The transformer provides galvanic isolation from low voltage level to medium level or high voltage level and provides stepping up or down of the output (secondary) voltage. At first, a design of three-phase medium frequency transformer is developed. The designed transformer is then validated using two-dimensional (2D) transient finite element analysis (FEA) and performance under the non-sinusoidal excitation is determined. After that, the optimization is carried out, for the set of selected design variables, in order to enhance the power density and efficiency of the targeted transformer. Finally, the performance of the full system, 3DAB converter, is determined using the parameters of optimized transformer. Also, two different rated input voltages for 4MW/1kHz threephase transformer are considered and analysed in this paper.