Abstract: Carving surface modeling is an important and complex process in digital art carving．To build up the smooth carving surface model suitable for digital art carving with fast speed and high quality,this paper proposes a modeling method based on planar closed graphs using quadratic Bézier curves and subdivision meshes．First,the constrained Delaunay triangulated closed curve is processed according to five cases．Then,the subdivision mesh surface covering the corresponding area is formed by building quadratic Bézier curves on the corresponding area and using straight lines to connect the subdivision points on all the Bézier curves along another direction．The experimental results show that this method can produce smooth carving surface models quickly and meet the actual demand of digital art carving．