On the basis of the 120 x 120 complete energy matrix, the local lattice structures of the octahedral (CrO6)(9-) clusters for Cr3+ ions doping in a variety of oxide crystals with D-3d or C-3 nu site symmetry have been studied by employing two distorted parameters, respectively. By simulating the calculated EPR and optical spectra data to the experimental results, the local lattice structure parameters are determined unambiguously. It is shown, by means of a series of calculations, that although the local lattice structures around the M (M = Al3+, Ga3+, Li+, Sc3+, etc.) ions in host crystals are obviously different, the local lattice structures of the octahedral (CrO6)(9-) clusters in a variety of oxide crystals doped with Cr3+ ions are similar and fluctuant in the vicinity of that of the Cr2O3. This may be ascribed to the fact that there is the similarly octahedral (CrO6)(9-) clusters in a variety of oxide crystals doped with Cr3+ and the Cr2O3 crystal. Our viewpoint is consistent with that of Gaudry et al. [Phys. Rev. B 2003, 67, 094108].