Rigorous coupled-wave analysis (RCWA) method is widely used in the critical dimension (CD) measurements and getting profile structure of two-dimensional periodic grating. In the application process, Fourier series expansion of formula for relative dielectric constant distribution in two-dimensional grating periodic unit is needed, but in the previous studies, the Fourier coefficient calculation formulas are only for several regular gratings, so the grating shape types whose diffraction analysis will be made by RCWA method are limited. To this restriction, new general Fourier coefficient calculation formulas for relative dielectric constant distribution in two-dimensional periodic grating are put forward by rectangular grid subdivision. They can be used for Fourier series expansion of relative dielectric constant distribution in arbitrarily shaped two-dimensional periodic grating and be used in RCWA method for diffraction problems.