Based on the diffraction theory, an analytical model for the beam quality after the beam passing through volume Bragg grating (VBG) is built. Considering the parameters of input beam and VBGs, the optical field distribution of an arbitrary beam passing through VBG after diffraction is analyzed，and the beam waist in second moment definition and the beam quality parameter of M2 can be calculated. The effect of space period of VBGs, input beam size, spectral bandwidth and initial input beam quality M2 on the diffraction beam quality are analyzed. The results show that the diffracted beam quality is influenced by the VBGs and the input sub-beam commonly. The spatial dispersion becomes larger with the decrease of period of VBGs, and the output beam quality after diffraction deteriorates significantly with the increase of input sub-beam size, spectral bandwidth and the initial beam quality. The model gives the analytical formula for the beam quality after diffraction, which can be used to obtain the beam quality after diffraction for different input beams easily and quickly. At the maximum input power of kilowatt level, the contribution of the initial M2 and the spectral line width to the diffracted beam quality is measured, and it is compared with the corresponding theoretical analysis.