For description of rotor-bearing system, a symmetrical flexible rotor supported by two turbulent journal bearings is modeled. The analysis of the rotor-bearing system is implemented under the assumptions of turbulent lubricant flow and a long bearing approximation. The bifurcation and chaos behaviors of the system are investigated for various rotational speeds. The motion equations are solved by the self-adaptive Runge-Kutta method. The numerical results show that the bifurcation of nonlinear responses of the system varies with the rotational speed of the rotor. It is found that the rich and complex dynamic behaviors of the system include period-1, period-doubling, quasi-periodic and chaotic motions etc.