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This study introduces a flywheel rotor support structure for an active magnetic suspension flywheel energy storage system. In this structure, there is an axial offset between the axial-bearing position and the mass-center of the flywheel rotor, which affects the tilting rotation of the flywheel rotor and which causes the coupling between its tilting rotation and radial motion. Therefore, the influence of the bearing position on the vibration characteristics of the flywheel rotor is explored in this paper. The tilting rotation constraint of the flywheel rotor by axial active magnetic bearing (AAMB) is analyzed, and the radial active magnetic bearing (RAMB) is equivalently treated with dynamic stiffness and dynamic damping. Based on this, a dynamic model of the active magnetic suspension rigid flywheel rotor, considering the position parameter of the axial bearing, is established. To quantify the axial offset between the position of the AAMB and the mass-center of the flywheel rotor, the axial-bearing position offset ratio γ is defined. The variation trend of the vibration characteristics of flywheel rotor with γ is discussed, and its correctness is validated through experiments. It is indicated that, with the increase of γ, the second-order positive precession frequency of the flywheel rotor decreases obviously, and the influence of the gyroscope torque gradually weakens. Meanwhile, its second-order critical speed ω_2c decreases significantly (when γ is 0.5, ω_2c decreases by about 62%); ω_2c corresponds to the inclined mode, revealing that the offset ratio γ has a prominent influence on the critical speed under this mode. In addition, as γ increases, the mass unbalance response amplitude of the flywheel rotor under the speed of ω_2c decreases significantly. The reasonable design of the axial-bearing position parameter can effectively improve the operational stability of the active magnetic suspension flywheel energy storage system. Full article