Tb-III-Cu-II-based single-molecule magnet (SMM) and non-SMM were synthesized to investigate the relationship between magnetic anisotropy and the symmetry of the ligand field by the reaction of [TbCu(o-vanilate)(2)(NO3)(3)] with methoxypropylamine (MeOC3H6NH2, 1) or ethoxyethylamine (EtOC2H4NH2, 2). In both complexes, Tb-III ions have a bicapped square-antiprism coordination geometry. When the Tb-III ion is in a less symmetrical ligand field, it has an easy-axis anisotropy and shows SMM behavior, whereas when it is in a more symmetrical environment, it has an easy-plane anisotropy and exhibits non-SMM behavior.