The EPR spectra of octahedral Fe3+ center in lutetium aluminum garnet have been studied by means of the complete energy matricesfor a d5 configuration ion in a trigonal ligand–field. It is manifested that the local lattice structure around an octahedrally coordinatedFe3+ center has an expansion distortion from that of undistorted host Al3+ ion. The expansion distortion can be ascribed to the fact thatthe radius of Fe3+ ion is bigger than that of Al3+ion, and consequently the Fe3+ ion pushes the oxygen ligands outwards. Simultaneously,for the octahedral Fe3+ center in the crystal, the local lattice structure parameters, R=(2.007±0.022)A andh=(52.708 ± 0.032), which reflect the interactions between impurity and crystal lattice, are determined from our calculation, andEPR parameters a, D, and (a-F) also get a unified explanation.