In this work, the ground state zero-field spitting of the tetragonal symmetry in KZnF3:Cr3+ has been studied using the Newman superposition model. The existence of Zn2+ -vacancy and the crystal lattice distortion has been verified. It is found that the contribution from the Zn2+-vacancy are non-negligible. Meanwhile, we obtain that the F- ion along [001] axis moves towards the central Cr3+ ion by Δ = 0.0029-0.0043nm. It has been verified also that the tetragonal center with D = - 0.2167cm-1 in KMgF3:Cr3+ is a CrOF5 cluster. To get agreement with the EPR experiment data it is necessary to introduce a contraction of the four fluorine ions in the plane perpendicular to the Cr3+-O2- axies pair, at the same time, the Cr3+ moves towards the O2- and the O2- moves towards the Cr3+ ion, but the displacement of the Cr3+ is larger than that O2- in CrOF5 cluster.