In this paper, the Bragg diffraction of SAW on acoustic grating is investigated by incorporating the anisotropy of the substrates. In the analysis, the difference between the incident wave, the fundamental wave and spatial harmonic wave in grating region and the diffraction waves in transmission region is phenomenologically described by using their different corresponding velocities. The experimental results for the diffraction of SAW on acoustic grating which is fabricated on Y-cut LiNbO3 are presented. The comparison of the experimental results with the analyzed results obtained on isotropy approximation shows that the discrepancy is significant. The "extraordinary Bragg diffraction" equations are obtained by using the coupled-waves method which takes the anisotropy of the substrates into consideration. It is shown that the calculated results based on "extraordinary Bragg diffraction" equations are coincident with the experimental results fairly well.