Abstract: Based on the geometric feature of spherically symmetric structures, a 3D rotation group, SO3, was constructed. By applying the group theory of complete set of calculation operators, the classified basis functions of this group,i.e.the spherical functions, were obtained through group transformations, being identical with ones obtained using the traditional variable separation method. The result shows that the basis functions of a spherically symmetric structure can be obtained completely through group transformations, and as a result, the research provide a new way to solve electromagnetic scattering problems with complicated boundaries by using the moment method.