A new method for three dimensional (3D) genus-zero shape classification is proposed. It conformally maps a 3D mesh onto a unit sphere and uses normal vectors to generate a spherical normal image (SNI). Unlike extended Gaussian images which have an ambiguity problem, the SNI is unique for each shape. Spherical harmonics coefficients of SNIs are used as feature vectors and a self-organizing map is adopted to explore the structure of a shape model database. Since the method compares only the SNIs of different objects, it is computationally more efficient than the methods which compare multiple 2D views of 3D objects. The experimental results show that the proposed method can discriminate collected 3D shapes very well, and is robust to mesh resolution and pose difference.