The pseudo-potential lattice Boltzmann method (LBM) with a tunable surface tension source term was applied to study a droplet impacting on a moving thin film. The effects of Reynolds number, Weber number and liquid film velocity on the evolution process of the liquid crown were analyzed. The results show that the initial liquid film velocity aggravates the kinematic discontinuity at the upstream liquid crown after impacting, leading to a dramatic deformation of the upstream liquid crown. However, the kinematic discontinuity in the liquid film at the downstream liquid crown is reduced, which can suppress the evolution of the downstream liquid crown. The upstream crown height increases with the increase of Reynolds number, but does not change with Weber number. The downstream crown height decreases with the increase of both Reynolds number and Weber number but the evolution process of the crown radius is not affected. Furthermore, with the increase of the initial liquid film velocity, both the upstream and downstream crown heights decrease, but the radius of the crown increases. The simulation results of LBM agree well with the experimental results and theoretical analysis, which proves that the pseudo-potential LBM is a robust and effective tool to simulate the process of a droplet impacting on a liquid film under complex conditions.