Morphing aims at gradually transforming a source object into a target one. Morphing techniques are of great importance in various applications, ranging from animations and movies to medical imaging and scientic visualization. In this work, we propose a new surface morphing algorithm dedicated to genus-0 models. Firstly, conformally map source and target surfaces onto the unit disk to get angle-preserving parameterizations. Secondly, compute the Möbius transformation of both angle-preserving parameterizations. Thirdly, compute the area-preserving parameterizations using optimal mass transportation map(OMT). Fourthly, we create a new, consistent mesh connectivity through surface remeshing strategy. Next, we adopt the radial basis function(RBF) to obtain feature alignment. Finally, linear interpolation is employed to generate intermediate surfaces. Our method preserves area element and enables users to fully control the size of in-between surfaces. The simplicity, eciency and ecacy of the proposed method are demonstrated by the experimental results.