Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated.In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite element method based on variational constraint approach is introduced because analytical bearing forces are not available.This method calculates the oil film forces and their Jacobians simultaneously while it can ensure that they have compatible accuracy.Nonlinear motion of the bearing-rotor system is caused by strong nonlinearity of oil film forces with respect to the displacements and velocities of the center of the rotor.A method consisting of a predictor-corrector mechanism and Newton-Raphson method is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of the bearing-rotor system.Meanwhile the dynamic coefficients of bearing are obtained.The nonalyzed by the Floquet theory.Chaotic motion of long term dynamic behaviors of the system is analyzed with power spectrum.The numerical results reveal such complex nonlinear behaviors as periodic, quasi-periodic, chaotic, jumped and coexistent solutions.