This paper deals with a new magnetic bearing in order to decrease a rotor eccentricity. The proposed bearing system consists of moving frames, suspensions, permanent magnets, electromagnets and Zero Power controller. The system enables to avoid rotor touchdowns. A clearance between a rotor and our proposed bearing may be increased compared to conventional electromagnetic bearings, since permanent magnets are used in new bearings. However, if Zero Power controller is applied to magnetic bearings, a severe problem emerges. When a levitating rotor is subjected to external steady force, to keep equilibrium between external force and magnetic force, a position of levitating rotor may be changed. To overcome this difficulty, this paper proposes a new magnetic bearing structure with moving frames and suspensions. The structure enables to decrease a rotor eccentricity, and a risk of contacting touchdown bearings with fixed frames is reduced. The paper shows the experimental results to verify the system.