Abstract: On the basis of the perturbation formulae of the g-factors (fourth-order) and the hyperfine structure constants (third-order) for a 3d9 ion in tetragonal symmetry (elongated octahedra), the spin Hamiltonian parameters for the Cu2+-doped LaSrAlO4 crystal are theoretically investigated. In the calculations, the tetragonal field parameters Ds and Dt are determined from the superposition model and the local structure of the impurity center; and the core polarization constant κ ≈0.286. Based on the studies, it is found that the calculated values show good agreement with the experimental data. In addition, the negative sign of A// is also determined theoretically.