The performance of power converter of electric propulsion aircraft (EPA), which should have high efficiency, high power density and high reliability, affects the volume, weight and efficiency of the whole electric aircraft (EA). This paper proposes a novel DC-DC converter with gallium nitride (GaN) transistors. Firstly, the working modes and main operation waveforms of the converter are analyzed. The new converter can achieve ZVS and ZCS through auxiliary soft switch branches. Compared with the traditional Buck-Boost converter, the soft switching capability of the proposed converter allows operation at very high frequency and has a higher efficiency. The multiphase interleaving magnetic integration technology is adopted to realize the modular design, which not only meets the requirements of high power and low ripple, but also eliminates right half-plane zero in boost mode, achieves high dynamic response and improves the power density. A novel parallel multiphase inverse coupled inductor (ICI) and a symmetrical array ICI are proposed, to allow a high-density and high-efficiency bidirectional DC-DC converter design for hybrid energy storage system of EPA. Finally, the proposed ICI prototype was compared with the state-of-the-art commercial ICI product, and the comprehensive performance of the converter was verified through steady-state, transient, efficiency and thermal experiments.