This paper proposes a novel radial hybrid magnetic bearing (RHMB), which has integrative magnetic pole boards and continuous working air gaps that reduce the hysteresis and eddy-current losses of the traditional homopolar structure. Its configuration and working principle are introduced. The bias and control magnetic circuits of the RHMB are analyzed with the equivalent magnetic circuit method. Mathematical models, from which the force-displacement and force-current relationships are derived, are built. The method for the rudimentary design of RHMB parameters is illustrated, through which a prototype RHMB for a reaction flywheel system is designed and assembled. Its performance and characteristics are calculated and analyzed with the obtained models and relationships. The results show that in its air gaps, the novel RHMB can generate a continuous and uniform bias magnetic field, which reduces the hysteresis and eddy-current losses and enhances the radial load capacity and axial passive resilience. The bias fluxes of all poles are decoupled from each other at all times. Although the control fluxes of the two channels are slightly coupled when the rotor is not in the central position, the coupling force-current stiffness is very low and can be ignored. These attributes simplify the design of the control system. The novel RHMB is especially suitable for high-speed and low-loss circumstances. A pair of RHMBs are used for the reaction flywheel, and for maintaining suspension of the rotor at the spin speed of 0-6000 rpm.