Facial features determination is essential in many applications such as personal identification, 3D face modeling and model based video coding. Fast and accurate facial feature extraction is still a filed to be explored. In this paper, an automatic extracting algorithm is developed to locate "key points" of facial features. The Delaunay Triangulation/Voronoi Diagram technique well known in computational geometric is applied on the edge enhanced binarized facial image. Facial features are classified and extracted in terms of various types of Delaunay triangles and the dual of a subset of the Delaunay triangles, Voronoi edges form the skeleton of facial skin. That is, facial feature's shape is described by Delaunay Triangulation/Voronoi Diagram. Furthermore, the facial features can be identified. The method succeeds in locating facial features in the facial region exactly and is insensitive to face deformation. The method is executable in a reasonably short time.