A coupled bending and torsion nonlinear dynamics model of rotor-bearing system was presented. The equations of unbalance rotor were established by the Lagrange approach and the coupled vibration characteristics of the rotor system with rub-impact was analyzed through numerical calculation. The bifurcation diagrams, waterfall plots, time domain charts, phase phane portraits and Poincaré maps were obtained to analyze dynamic characteristics of the system and the results reveal multiform complex nonlinear dynamic behavior of the rotor-bearing system with rub-impact. Moreover, the influence of the damping ratio on the vibrations of the rotor system was analyzed. These analysis results of the present paper provide the theoretical bases for the rotor system’s status recognition, diagnosis and safe and economic operation.