Three EPR g-factors for orthorhombic Ce3+ centers in Y3Al5O12 and Lu3Al5O12 garnets have been investigated by a complete diagonalization (of energy matrix) method (CDM) and the local structure around Ce3+ ion in the two garnets are also obtained and compared with those calculated by first principles. The calculated EPR g-factors are in good agreement with the experimental values. The link between g-factors and local structure of doped Ce3+ ion in the two garnets is studied by perturbation method (PTM) and the present CDM, respectively. The intrinsic discontinuous properties of PTM to calculate EPR g-factors are shown clearly in this Letter. (C) 2012 Elsevier B.V. All rights reserved.