The response characteristics of the bi-swirl coaxial injector under oscillating backpressure were investigated numerically based on coupled level-set and volume of fluid model. The backpressure oscillation frequency was set ranging from 1000 to 5000 Hz. The frequency and amplitude response characteristics of liquid films were analyzed under different injection conditions. The amplitude of the pressure response inside the injector was determined by the acoustic damping of the system. Due to the central gas core inside the inner injector, the inner injector manifold was found to be more sensitive to the backpressure oscillation. The frequency characteristic of the liquid film response indicated the presence of the characteristic frequency where the response amplitude was maximum. This characteristic frequency was linearly positively correlated with the mass flow rate of the inner injector, while the flow in the outer injector could suppress the response amplitude of liquid films. Meanwhile, the nonlinearity of the response was dominated by the inner liquid film and was also the strongest at the frequency with the highest response amplitude. The simulated flow fields showed that the oscillation of the ambient airflow periodically hindered the liquid film, leading to Klystron effect. Finally, it was suggested that the characteristic frequency was related to the axial velocity of the inner liquid film at the injector outlet and the acoustic length of the gas core. In addition, the response amplitude of liquid films was found to be controlled by the spray cone angle and the total mass flow rate of propellants.