Abstract: Firstly, the solutions of vector wave equation in isotropic medium are obtained by the Debye potential functions under the spherical coordinates. Then, the reflection and transmission process of in-coming and out-going waves in single layer and in spherically multilayered media are analyzed, and the corresponding reflection coefficients, transmission coefficients, the generalized reflection coefficients and generalized transmission coefficients are gained. Next, the Debye functions produced by source at different places in spherically multilayered media are achieved. Finally, the electric type of dyadic Green's functions and the magnetic type of dyadic Green's functions are expressed by the vector wave functions under the spherical coordinates based on the Debye potential functions obtained.