Labyrinth seals are widely used to prevent fluid leakage in high-low pressure areas of the rotating machinery. However, the rub-impact fault easily occurs in labyrinth seals. Considering the influence of gyroscopic effect, a finite element model of seal-rubbing rotor system is established in this study based on the Muszynska seal force model, the rolling bearing force model, and the nonlinear rubbing force model. The vibration characteristics under the coupling faults of airflow excitation and rub-impact are analyzed. First, the response of the system without rub-impact fault is simulated numerically and verified by experiments. Subsequently, the dynamic characteristics of the rotor under the conditions of slight and severe rub-impact faults are analyzed. Finally, the influence of the rub-impact parameters is further studied. The results indicate that when the rub-impact fault is absent, airflow excitation occurs at a certain speed, which exhibits the characteristics of frequency locking and combination frequency. The coupling dynamic responses of airflow-induced vibration and rub-impact fault show a rich spectrum of nonlinear phenomena, which are closely related to the degree of rub impact. This study may provide a theoretical basis for the detection and diagnosis of fluid-induced rub-impact fault in labyrinth seal-rotor systems.