The aromatic copolyester of 4-hydroxybenzoic acid (HBA) and 6-hydroxy-2-naphtoic acid (HNA) shows strong SHG-activity in the nematic phase as well as the crystalline phase in spite of no absorption in the visible region. Ab initio quantum chemistry calculations of the copolyester have been carried out in order to clarify the origin of this strong SHG-activity. The second-order hyperpolarizability of the HBA dimer is comparable to that of p-nitroaniline and it increases with the degree of polymerization. The large hyperpolarizability of the aromatic polyester is ascribed to the large electronic transition moment.