A novel deformable model for 3D surface extraction, called growing deformable surface patches, is presented in this work. In the proposed method, a growing mechanism is introduced to 3D deformable model. With the growing framework, the proposed deformable model could achieve topologically adaptable surface extraction by connecting new surface patches and active patches and automated triangulating the square patch in particular situations. A number of experiments demonstrate that the proposed algorithm can extract the surface of complex anatomic structures effectively. Compared with the existing topologically adaptable deformable surfaces, computational cost is reduced because no splitting or merging judgement is carried out among all the vertices in each deformation step. Topologically adaptable detection is achieved by analyzing the possibility of patch connection among the "active" surface patches only.