A least square particle finite element method is presented and used to simulate the impact and splash of 2D water droplets on the water surface. This algorithm is based on an upgraded Lagrangian framework. An extended Delaunay triangulation method is used to get the new mesh at every time step. An alpha-shape method is used to deal with the splash and impact of the free surface. The least square finite element method is applied to solve the Navier-Stokes equations. An adaptive time step algorithm is derived to improve the efficiency and the robustness of calculation，and a mesh pulling scheme is introduced to improve the conservation of the total mass. Finally，when compared with the commercial Flow-3d code，the computational results achieve good agreement. Moreover，the free surface is more accurate and more clearcut than that of the Eulerian description based Flow-3d code.