Using the plane-wave method, we calculate the band structures and transmission characteristics of the three-dimensional fcc photonic crystals. For a SiO2 opa l photonic crystal, we calculate the energy spectrum and the transmission featu re of electromagnetic waves along the [111] direction using both the plane-wave method and the transfer-matrix method, the obtained results are consistent wit h each other. For a full band gap studies of the inverse-opal structure, the co nvergence effect in the plane-wave method on the calculation is discussed. For an fcc lattice of core-shell sphere, it is shown that the relative L-gap width of a suitable coating of dielectric spheres of a lower dielectric material can increase by 50% as compared with that of homogeneous high-dielectric spheres. We also find that the optimum radius ratio between interior and entire spheres is 0.69.