Abstract: Based on the two features of the Delaunay triangulation：maximum and minimum feature，empty circumcircle feature，in this article the procedure of building triangulation network needs three steps：creating boundary，building up the interior triangulation network，coping with the hole between the boundary and the interior triangulation network.The detial process is that we can build up the boundary throught the boundary point set at first，then we can form the inside nework by the method of variance and aera growth—inserting the non-boundary points，at the last，we shall deal with the hole between the boundary and the interior network boundary in the method of equal proportion partition.After the improvement，we needn’t judge the new born edges and the points are whether or not belonged to the boundary，and avoid the complex process，acquire the Delaunay triangulation surface of the object quickly.Experiment results demonstrate that the method proposed is simple and effective.