Abstract: Presents an algorithm for the triangulation of point-sets in an arbitrary polygon. The algorithm adopts the procedure by first looking for the convex hulls layer by layer especially the vertices in the polygon not lying at the edges of the convex hulls; then cutting the ring domains into the sequence of the trilateral, and finally optimizing the length of the edges of every trilateral, and changing the cutting procedure to achieve the triangulation of the shortest(or close to the shortest).