Aiming at the problem that the surfaces with some edge features are difficult to reconstruct correctly, a method for reconstruction of sharp feature surfaces is proposed based on intersection of meshes extension. Firstly, sharp feature points are removed by Gauss map clustering, and the remaining points are segmented by seed point growth algorithm. Then, to improve the smoothness of surfaces continuation areas, the bound- ary sample points after gain optimization are taken as the local sample of surfaces, and the points are ex- tended with the extended direction of the cubic Bézier curve as the guidance. Finally, the reconstruction re- sults of the extended flat areas are intersected, and sharp features are reconstructed by the method of surfaces trimming. The experimental data of surface reconstruction from the sampling points provided by Stanford University, the results show that this method can effectively avoid the occurrence of errors such as holes and edge notches, and has good adaptability to non-uniform sampling data.