The pseudopotential lattice Boltzmann method (LBM) with a tunable surface tension term is applied to study a droplet impact on a moving thin film. The Re effects of dimensionless parameters on the upstream and downstream crown evolution are studied, including Reynolds number (Re), Weber number (We), liquid film thickness, and horizontal velocity of the liquid film. The movement of the liquid film causes the asymmetry development of the upstream and downstream crown. Both the instability of upstream and downstream crowns increases with the increase of Re and We, and the upstream crown becomes more prone to break up. And a critical value of film thickness exists with the height of the upstream and downstream liquid crowns reaches the maximum value. And the velocity of liquid film restrains the development of the height of the upstream and downstream crowns, but it promotes the growth of the crown radius.