Abstract The dependence of the EPR g-factors on the local structural parameter for a 4f11 configuration ion Er3+ in a trigonal crystal-field has been studied by diagonalizing the 364×364 complete energy matrices. Our studies indicate that the EPR spectra of the trigonal Er3+–VK centers in KMgF3 and KZnF3 may be attributed to the translation of the cubic Kramers doublet Γ7. Furthermore, the EPR g-factors of the trigonal Er3+–VK centers may be interpreted reasonably by the shifts ΔZ≈0.340 A and ΔZ≈0.303 A of the Er3+ ions toward the charge compensator VK along the C3 axis for the KMgF3:Er3+ and the KZnF3:Er3+ systems respectively.