To improve the coverage accuracy and efficiency of the satellite, the geometric characteristic related to satellite coverage of a ground region is analyzed, and the division method for space geometric configuration of constellation is mainly studied based on the properties of the Delaunay triangulation and the Voronoi Diagram. Subsequently, the constellation coverage problem is simplified into multiple one-satellite coverage problems by defining the coverage area of each satellite. Furthermore, an accurate and effective approach to solve the satellite constellation coverage problem for any type of coverage area is put forward. Finally, the comparison of accuracy and efficiency between the proposed approach and the classic Grid-point method is given for different target areas. The test result shows that the proposed method is valid and more efficient. The proposed method can also be used in satellite constellation optimization design and performance evaluation.