For the application into a 1 kWh flywheel energy storage system(FESS), this paper presents the design scheme of radial and axial hybrid magnetic bearings which use bias fluxes generated by permanent magnets. In particular, the axial hybrid magnetic bearing is newly proposed in this paper, in which a permanent magnet is arranged in axial direction so that it can support the rotor weight as well as provide a bias flux for axial magnetic bearing. Such hybrid magnetic bearings consume very low power, compared with conventional electromagnetic bearings. In this paper, to stably support a 140 kg flywheel rotor without contact, design process is explained in detail, and magnetic circuit analysis and three-dimensional finite element analysis are carried out to determine the design parameters and predict the performance of the magnetic bearings.