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The electron paramagnetic resonance spectrum of the KMgF3:Fe3+ system has been studied on the basis of the complete energy matrices for the electron-electron repulsion, the ligand-field and the spin-orbit coupling of d(5) configuration ion with a trigonal symmetry. A two-layer-ligand model, which includes six F- ions in the first layer and eight next nearest-neighbor K+ ions in the second layer, has been proposed to describe the real ligand-field. By simulating the second-order and fourth-order EPR parameters D and (a - F) simultaneously, a displacement of a K+ ion along C-3-axis towards the Fe3+ ion has been found theoretically, and this displacement will give rise to the distortion of the octahedron constructed by six F- ligand ions in the first layer. Delta Z is used to describe the displacement of a K+ ion along C3-axis towards the Fe3+ ion, and two angles theta(1) and theta(2) between the Fe3+-F- band and C3-axis are taken to describe the local distortion along the [111] direction. By adjusting the Delta Z, the range of the local distortion parameters Delta theta(1) = 5.54 degrees-6.07 degrees, Delta theta(2) = -4.60 degrees to -5.00 degrees are determined, and the EPR spectrum of the KMgF3:Fe3+ system has been satisfactorily explained by the two-layer-ligand model. (c) 2006 Elsevier B.V. All rights reserved.