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A dynamic model was set up for a two-span and rotor-bearing system with crack fault. Using the continuation-shooting algorithm for periodic solution of nonlinear non-autonomous system, the stability of the system periodic motion was studied by the Floquet theory. The periodical, quasi-periodical and chaos motions were found in the system responses. The unstable form of the rotor system with crack fault is period-doubling bifurcation. There are unstable forms of period-doubling bifurcation and Hopf bifurcation in different rotate speed. There are many harmonic elements of 1/3, 1/2, 2/3, 1, 2 and so on within the sub-critical speed range. But the 2-harmonic element decreases within the super-critical speed range. The results from this work provide a fundamental basis for the failure diagnosis of the rotor-bearing system.