The vector wave functions satisfinga vector homogeneous Helmholtz equation are introduced as the basic vectors, and the field both outside and inside the grooves of the grating are expanded by vector plane wave functions and vector modes respectively. Equations of the amplitudes which can be solved numerically are dirived.The method can be used to study the diffraction of optical plane waves, the incident direction and the polarization of which can be arbitary. The results for P- and S-polarization are are consistent with that published before.