This paper first construct 2D principal manifold of the 3D point cloud which is typically unoriented and unevenly distributed in space, and give the quadratic optimized approximation of principal manifold in form of watertight mesh with spherical homeomorphism. By this method, the shape description of 3D point cloud is converted into the description of 2D principal manifold evenly spread in spherical parameter field. Then, it applies translation, rotation and scaling to the quadratic optimized mesh to align the mesh polar axis, denoting this process as initial rough alignment. Finally, the ICNP (iterative closest normal point) algorithm is used to iteratively refine the rigid transformation to bring the two meshes into the best alignment with respect to the least mean square error, and the alignment error is recorded as difference distance between two 3D point clouds. The experimental results show that the proposed 3D point cloud shape description based on quadratic optimized approximation of 2Dprincipal manifold is robust to noise and resolution, and can be used as the shape descriptor for 3D retrieval.