This paper focusses on the heterogeneous nucleation on the surface with the non-constant curvature. The formation of a spherical nucleus on the ellipsoid of rotation is considered. Following the classical nucleation theory, the work of formation of a critical nucleus on the ellipsoid of rotation has been given, and the effects of geometry sizes and the material properties of the ellipsoid of rotation on the work of formation of a critical nucleus have been obtained. When the geometry size of the substrate is about value of the critical nucleus radius, there may exist twice nucleation on the ellipsoid of rotation for the case of the smaller value of lambda and phi < pi/2. As the work of formation of a nucleus has only one extremum (the maximum), the nucleation on the oblate rotational ellipsoid is more easy than on the spherical surface, while nucleation on the prolate ellipsoid of rotation is more difficult than on the spherical surface. Furthermore, if the particles of the ellipsoid are added into the parent phase as nucleation agents or catalysts, for some geometry sizes, they would not have the effects on the heterogeneous nucleation. (C) 2016 Elsevier B.V. All rights reserved.