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The local structure of the tetragonal Er3+ center in CaO is theoretically studied by using the perturbation formulas of the g factors for a 4f(11) ion in tetragonal symmetry. In these formulas, the contributions to the g factors from the second-order perturbation terms and the admixtures of various states are taken into account. Based on the investigations, this center is suggested to be the impurity Er3+ substituting the host Ca2+ site, associated with a Ca2+ vacancy V-Ca in the [100] (C-4) axis due to charge compensation. By studying the g factors of the tetragonal center, impurity Er3+ is expected to undergo an off-center displacement Delta Z( approximate to 0.2 A) towards the V-Ca along the C-4 axis because of the electrostatic attraction. The calculated g factors based on the displacement Delta Z show reasonable agreement with the observed values.