Abstract: A new prediction method for periodic solutions of unbalanced bearing rotor system is provided,which uses the steady state and transient state information of the periodic solutions to solve Jacobi matrix.Then this method can predict and trace the periodic solution of the system.At the same time,the Floquet multiplier of the periodic solution can be obtained from Jacobi matrix to judge its nonlinear stability.Because the steady state and transient state information of the periodic solution can be observed in practice,the method would be used widely.A rigid unbalanced bearing rotor system is taken as an example,the T periodic solution of this system is predicted and traced.