The local structure of the trigonal Co 2 + center in MgTiO 3 is theoretically investigated by using the perturbation formulas of the spin Hamiltonian parameters for a 3d 7 ion in trigonal symmetry based on the cluster approach. From the studies, it can be found that the impurity Co 2 + ion substitutes for Mg 2 + rather than Ti 4 + ion, and that the Co 2 + takes an outward displacement (~0.02A) away from the center of the oxygen octahedron along the C 3 axis in MgTiO 3 . The theoretical spin Hamiltonian parameters calculated from the above displacement show good agreement with the observed values. The validity of the results is discussed based on the impurity displacement model for corundum-type structures.