Barium borate (β-BaB2O4) is a new type of nonlinear optical crystal which wag made by China for the first time. Its transparent range of 190～3000 nm and SHG coefficient of macroscopic crystal x111(2w) = 4.6×10-9 e. a. u. have been shown by experiments. CNDO/S calculated value of x111(2w), which was in good agreement with the experiments was obtained, however, the calculated ultraviolet absorption edge 90 nm was far from the result of experiments. In this paper we report one-electron energy spectra of some inorganic and organic aromatic rings based on EHMO theory. Both calculated values of SHG coefficients and ultraviolet absorption edge for Barium borate crystal are in good agreement with the experiments. Since there has been dispute oil the position of ultraviolet absorption edgo we also calculate it by using more accurate SOF-Xa-SW method and the calonlated result gupports the EHMO oaloulation mentioned above. The factors which determine tho position of ultraviolet absorption edge and the values of the SHG coefficients are discussed briefly