, KTaO 3 .Based on the defect models that the two tetragonal Cu 2+ centers in KTaO 3 are due to Cu 2+ ions at Ta 5+ sites associated, respectively, with one and two oxygen vacancies (V 0 ) along C 4 axis because of charge compensation, the spin-Hamiltonian parameters (g factors g // , g ⊥ and hyperfine structure constants A // , A ⊥ ) of both Cu 2+ centers in KTaO 3 are calculated from the perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM). The calculated results from both theoretical methods are not only close to each other, but also in reasonable agreement with the experimental values. This suggests that both methods are effective in the explanations of spin-Hamiltonian parameters for 3d 9 ions in tetragonal symmetry. From the calculations, the defect models are confirmed and the defect structural data are obtained for both Cu 2+ centers in KTaO 3 .