Abstract: Based on the crystal-field theory, the anisotropic g factors of the trigonal Ru3+ center in α-Al2O3 are theoretically studied by using the perturbation formulas of the g factors for a 4d5 ion in trigonal symmetry. In these formulas, the orbital reduction factor k and the spin-orbit coupling parameter ζd for the impurity Ru3+ in the crystal as well as their contributions to the g factors are taken into account in a uniform way. The calculated results show good agreement with the experimental data. In addition, the local structure property of the impurity center is also discussed.