A dynamic model was set up for the two-span rotor–bearing system with coupling faults of crack and rub-impact. 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 unstable form of the rotor system with coupling faults is Hopf bifurcation when the depth of crack is smaller. The influence to the response of the system increased along with the depth of crack, the unstable form of the rotor system with coupling faults is period-doubling bifurcation. The conclusions provide theoretic basis reference for the failure diagnosis of the rotorbearing system.