In this paper, we present a modified smoothed particle hydrodynamics (SPH) method. The kernel approximation and the particle approximation are corrected to ensure that polynomial functions are exactly interpolated up to a given degree. Riemann solver is adopted to solve equations of fluid motion. A surface tension calculation program is used for considering the surface tension effects in droplets splashing. The process of droplet impact on liquid surface is numerically simulated by the modified smoothed particle hydrodynamics method. The numerical results clearly demonstrate that the modified SPH method can effectively describe the dynamics of droplet splashing and the variation of the free surface, and that the accuracy of the results can be stable.