A rigorous coupled wave theory for the Bragg diffraction of a Gaussian beam in the uniaxial crystal is derived and a group of rigorous coupled wave equations and diffraction efficiency formula are obtained in terms of the proper coordinate transformation and Riemann method. The relations between the efficiency and the index modulation, the wavelength selectivity and the angular selectivity are discussed. At the same time, the requirement of the efficiency on width of the reconstruction beams is also analyzed. Simulation calculations show that, for the extraordinary to extraordinary (ee) Bragg diffraction, the possible maximum efficiency is determined by the incident angle of the recording beams. Moreover, by choosing every parameter properly, the theoretical efficiency can reach approximately 90% in the very low index modulation such as 8.2×10-5 for ee type Bragg diffraction. This model may give a theoretic guidance for how to obtain high efficiency in the low index modulation condition.