Gas–cyclone body coupling vibration is one kind of vibration caused by air pulsation. This coupling vibration causes widespread damage and deformation of three-stage cyclone separator used in residue fluid catalytic cracking. After theoretically analyzing the mechanism of the generation of the gas–cyclone body coupling vibration, the numerical simulation of three-dimensional swirling flow the cyclone separator was performed by using Reynolds stress model (RSM). The results showed the existence of precessing vortex core (PVC) in the cyclone separator. The PVC phenomenon and motion of PVC were described in detail. Furthermore, the amplitude and frequency of gas fluctuation in the PVC region at different axial positions were quantitatively analyzed. The simulation results agreed with the experimental results of laser Doppler velocimetry (LDV). Finally, characteristics of PVC in cyclone separator with a novel vortex finder were designed, and the results showed that the novel vortex finder can reduce flow vibration.