In this paper, we present a modified smoothed particle hydrodynamics (SPH) method. In order to well predict the morphology change of liquid drop, the presented SPH method employs a kernel gradient correction and a coupled solid boundary treatment algorithm. An inter-particle interaction force is used to model surface tension, and an artificial stress model is used to deal with tensile instability. The process of droplet impacting on liquid film is numerically simulated by the modified SPH method, which can well predict the pressure field evolution process of the drop impacting onto the liquid film and capture the variation of the free surface at different instants. Effects of Web number and surface stress on droplet impacting are also investigated, and mechanism of droplet splashing is analyzed. It is clearly demonstrated that the modified SPH method can effectively describe the dynamics of droplet splashing and the variation of the free surface. The obtained liquid drop morphology accords well with the results from other sources.