The molecular equilibrium structures, electronic structures, and one-and two-photon absorption (TPA) properties of C-2v (Zn(II), Fe(II) and Cu(I)) dipolar and D-2d (Zn(II) and Cu(I)) and D-3 (Zn(II)) octupolar metal complexes featuring different functionalized bipyridyl ligands have been studied by the ZINDO-SOS method. The calculated results show that one- and two-photon absorption properties of metal complexes are strongly influenced by the nature of the ligands (donor end groups and pi linkers) and metal ions as well as by the symmetry of the complexes. The length of the pi-conjugated backbone, the Lewis acidity of the metal ions, and the increase of ligand-to-metal ratio result in a substantial enhancement of the TPA cross sections of metal complexes. Substitution of CN and NN for CC plays an important role in altering the maximum TPA wavelengths and the maximum TPA cross sections of metal complexes. Of them, the CN substituted metal complexes have relatively large TPA cross sections. Replacing styryl with thienylvinyl makes the one-photon absorption wavelength red shift and at the same time leads to a great decrease of the maximum TPA cross sections of metal complexes. The possible reason is discussed. In the range 500-1250 nm, octupolar metal complexes exhibit intense TPAs and therefore are promising candidates for TPA materials.