Flux avalanches induced from thermomagnetic instability are crucial challenges for the application of superconducting thin film devices. In this paper, flux avalanches in a type-II superconducting thin film exposed to a transient AC magnetic field are numerically simulated by solving the coupled nonlinear Maxwell's equations and the heat diffusion equation based on the fast Fourier transform (FFT) method. The dependence of the threshold magnetic field on the ambient temperature, film thickness and magnetic field ramp rate are obtained through these numerical simulations, which show good agreement with experimental results. A linear increase in the threshold field as the film thickness increases and a nonmonotonic increase in the threshold field as the ambient temperature increases have also been found. Our numerical results demonstrate that the threshold field decreases exponentially as the ramp rate increases. Flux avalanche patterns observed in magneto-optical imaging (MOI) measurements for a film exposed to an AC magnetic field are reproduced. The hysteresis magnetization and maximum temperature jump curves are also illustrated. We find that fingering instability plays an important role in the thermomagnetic response of superconducting thin films under transient AC magnetic fields, especially for high magnetic field ramp rates.