In the present paper, the characteristics of Mega-Flux$^{(R)}$, JNEX-Core$^{(R)}$, amorphous and ferrite cores are compared to the inductor of buck-boost converters for Hybrid Electric Vehicles. Core losses are analyzed at the condition of 10 kHz sine wave excitations, and permeability fluctuations vs. temperature and magnetizing force will be analyzed and discussed. Under the specifications of the buck-boost converter for 20 kW THS-II, the power inductor will be designed with Mega-Flux$^{(R)}$ and JNEX-Core$^{(R)}$, and informative simulation results will be provided with respect to dc bias characteristics, core and copper losses.