The electronic structural and optical properties of Poly (ethylene terephthalate) (PET) are studied based on first principle method of density functional theory. It shows that molecules orbit contribution of PET are derived from carbon 2p orbital and oxygen 2p orbital, respectively. However, the band gap from the energy band structure is much smaller than that of the experimental value. For the highest occupied molecular orbital, the charge density is mainly distributed in the both sides of the benzene ring . However, for the lowest unoccupied molecular orbital, the charge density is mainly distributed on the benzene ring. The band gap calculated from the absorption edge of absorption spectra is in agreement with the result of the energy band structure. Furthermore, the relationship between the formation of dielectric function peaks and other spectral characteristics is interpreted.