A rotor supported by a superconducting magnetic bearing (SMB) shows complicated behavior because of nonlinear magnetic force. In a large-scale system, magnetization distribution of its rotor can be non-uniform. This non-uniformity can cause some nonlinear vibrations of the rotor. In this study, we investigated dynamical behavior of a rotor whose geometric and magnetic centers were not identical. We derived its equations of motion and found out that they had nonlinear terms including quadratic terms. It can be noted that these terms can cause nonlinear vibration such as superharmonics and subharmonics. We experimentally verified our prediction and confirmed appearances of the 2nd and the 3rd order superharmonics and the 1/3-order subharmonics due to the nonlinearity of the magnetic force.