Using the normal vector wave functions, which satisfies the vector homogeneous helmholtz equation, as the basis vectors, the fields inside the grooves of the grating are expanded by the vector modes, while the fields outside of the grooves are expanded by the vector pseudoplane wave functions. Applying field coupling conditions, diffraction equation for the amplitudes are derived. The method can be used to study the diffraction of optical plane waves with arbitrary incident direction and polarization direction. The results for the special cases of P-and S-polarization are well consitent with that given by Ref.[6].