Based on the nonlinear dynamics theory, the unbalanced response and corresponding bifurcation behavior of the rotor dynamic system supported by gas journal bearings are investigated. A time-dependent mathematical model is used to describe the pressure distribution of gas journal bearing with nonlinearity. The model of rigid Jeffcott rotor with self-acting gas journal bearing supports is built. The finite difference method and the successive over relaxation (S. O. R. ) method are employed to solve the time-dependent Reynolds equation of gas journal bearings. The unbalanced responses and bifurcation of the rotor dynamic system supported by finite gas journal bearings are analyzed by orbit diagrams, Poincaré map diagram, time series diagram, frequency spectrum diagram and bifurcation diagram. The numerical results reveal the rich and complex nonlinear behaviors of the system, such as periodic, period-doubling, and chaotic motion, and so on.