The dynamic model and nonlinear dynamic equation of rotor-bearing system are established based on rotor dynamics. Combining the Newmark method, the predictor-corrector mechanism and Newton-Raphson method, a solution to the unbalanced response of dynamics system are obtained. With the lubricant dynamic viscosity of flexible rotor bearing as the control parameter, nonlinear dynamic responses of rotor system are determined. The stability of the rotor unbalance response cycle is analyzed on the basis of Floquet bifurcation theory and Poincaré map. Numerical results indicate that the system has nonlinear phenomena of periodic motion, 2- periodic motion, 4- periodic motion etc.