The defect structure for Ni3+ in ZnO crystal is theoretically investigated using the perturbation formulas of the spin Hamiltonian parameters for a 3d7 ion in trigonally distorted tetrahedra. In view of the significant covalency of the system due to the high valence state of Ni3+, the ligand orbital and spin-orbit coupling contributions are taken into account in a uniform way based on the cluster approach. The impurity Ni3+ is found not to occupy the ideal Zn2+ site in ZnO but to undergo the small axial displacement of about 0.044 Ǻ away from the oxygen triangle along the C3 axis. The theoretical spin Hamiltonian parameters based on the above impurity displacement show good agreement with the experimental data. The defect structure of this impurity center is compared with that for the similar Fe3+ in ZnO.