Conventional ball bearing reaction wheel used to control the attitude of spacecraft cant absorb the centrifugal force caused by imbalance of the wheel rotor, and there will be a torque spike at zero speed, which seriously influences the accuracy and stability of spacecraft attitude control. Compared with traditional ball-bearing wheel, noncontact and no lubrication are the remarkable features of the magnetic bearing reaction wheel, and which can solve the high precision problems of wheel. In general, two radial magnetic bearings are needed in magnetic bearing wheel, and the design results in a relatively large axial dimension and smaller momentum-to-mass ratios. In this paper, a new type of magnetic bearing reaction wheel(MBRW) is introduced for satellite attitude control, and a novel integrated radial hybrid magnetic bearing(RHMB) with permanent magnet bias is designed to reduce the mass and minimize the size of the MBRW, etc. The equivalent magnetic circuit model for the RHMB is presented and a solution is found. The stiffness model is also presented, including current stiffness, position negative stiffness, as well as tilting current stiffness, tilting angular position negative stiffness, force and moment equilibrium equations. The design parameters of the RHMB are given according to the requirement of the MBRW with angular momentum of 30 N · m · s when the rotation speed of rotor reaches to 5 kr·min. The nonlinearity of the RHMB is shown by using the characteristic curves of force-control current-position, current stiffness, position stiffness, moment-control current-angular displacement, tilting current stiffness and tilting angular position stiffness considering all the rotor position within the clearance space and the control current. The proposed research ensures the performance of the radial magnetic bearing with permanent magnet bias, and provides theory basis for design of the magnetic bearing wheel.