Abstract: The band gap structure of face-centered cubic lattice of 3-D photonic crystal with sphere scatter was studied with the plane wave expansion method. The energy bands of the air sphere in medium and the medium sphere in air with different parameters were calculated. The results obviously prove that the wholly band gap of air sphere in medium will never exist at any parameter, and the wholly band gap of medium sphere in air will exist when suitable parameters are chosen. The relation between the width of band gap and the air sphere's radius is similar to that of the substrate's dielectric constant, while the relation between the band gap's center position and the radius of air sphere is dissimilar to that of the dielectric constant of the substrate. The conclusion extends and renews the relative fields.