The spontaneous emission spectra of semiconductor planar micro-cavities are calculated by Taylor series with high order and new variable.An approximation of spontaneous emission with TE mode in a planar micro-cavity with half wavelength and high reflectivity is obtained. In the planar semiconductor micro-cavities,combined with Fermi-Dirac distribution functions of electrons and holes,the spontaneous emission spectra in a small angle and all directions calculated are agree well with those by numerical integral.The approximation can be used to the spontaneous emission spectra in QW(quantum well) planar micro-cavities.