Based on the three- dimensional coupled wave theory, the theory of diffraction of local volume holographic gratings recorded with arbitrary polarization plane waves is studied. Simple analytical expression for the amplitude profiles of the main component and cross component of transmitted and diffracted waves are obtained. The influence of the polarized azimuths of the incident wave during recording and reconstruction on the amplitude of the transmitted and diffracted waves is discussed. It is demonstrated that the conversion is seen to proceed more quickly for reducing the polarized azimuth at recording, but the output beam deviates more and more from the uniform amplitude distribution. It is also shown that owing to the different coupling values of between the diffracted and incident beams inside the grating from different directions of the electric vector, the amplitude profiles of the main component and cross component of the output beam are different from each other when the polarized azimuth at reconstruction is different.