Here we present a theory which predicts the process of ultraviolet generation by frequency doubling of focused green Gaussian beam in BBO crystal. In this theory, phase matching acceptance angle, walk-off angle and the divergence of fundamental beam have been considered. Numerically computed results show that the variations of the waist of Gaussian beam can lead to changes in conversion efficiency and in the ultraviolet transverse intensity distribution of far-field. Comparison between the numerical simulation and experimental results supported our theoretical analysis.