Based on the nonlinear theory, the unbalanced response behavior of the rotor dynamic system supported by gas journal bearings is investigated. A time-dependent mathematical model is established to describe the pressure distribution of gas journal bearing with nonlinearity. The rigid Jeffcott rotor with self-acting gas journal bearing supports is modeled. The differential transformation method is employed to solve the time-dependent Reynolds equation of gas bearings. The unbalanced responses of the rotor system supported by finite width gas journal bearings with three axial grooves are analyzed by bifurcation diagram, orbit diagram, Poincaré map diagram and frequency diagram. The numerical results reveal periodic, period-doubling, period-4, period-8 and chaotic motion of nonlinear behaviors of the system.