Considering the effect of a squeeze film damper (SFD), the dynamic characteristics of a rotor system with rubbing fault, misalignment rubbing coupling faults, and control of chaotic motion of the system with SFD are investigated. Based on the Lagrange equation, a dynamic model is set up for the SFD rotor- ball bearing coupling system with misalignment rubbing coupling faults. The model is solved using the Runge-Kutta method. A bifurcation diagram, Poincaré diagram, and spectrum diagram are used to compare and analyze. The results show the following: The SFD under a reasonable film gap can effectively suppress the nonsynchronous response and vibration amplitude of the rotor system, which can control the fault rotor system to stabilize periodic orbit. If the film gap is excessively small, it will form a strong nonlinear film supporting force and produce a nonconforming spectrum, which will lead the stable periodic system back to chaos. In addition, the 2X, 3X, 4X, 5X typical spectrum amplitudes are generated by the misalignment fault. When the film gap is reduced, SFD has different effects on these amplitudes. Among them, the amplitude of the 2X spectrum changes the most, the amplitude of the 3X and 4X spectrum changes less, and the amplitude of 5X is essentially unchanged.