The electron paramagnetic resonance (EPR) parameters (g factors g∥, g⊥ and hyperfine structure constants A∥, A⊥) and the local structure of the tetragonal Cu2+ center in trigonal ZnSeF6·6H2O crystal are theoretically investigated from the perturbation formulas of these parameters for a 3d9 ion in tetragonally elongated octahedra. In the calculated formulas, the contributions to the EPR parameters from ligand orbital and spin–orbit coupling are included on the basis of the cluster approach in view of moderate covalency of the studied systems, the required crystal-field parameters are estimated from the superposition model, which enables correlation of the crystal-field parameters and hence the EPR parameters with the tetragonal distortion of the studied [Cu(H2O)6]2+ cluster. According to the calculations, the ligand octahedra around Cu2+ are suggested to suffer relative elongation τ (≈ 0.085 Å) along the [001] (or C4) axis for the tetragonal Cu2+ centers in ZnSeF6·6H2O crystal, due to the Jahn–Teller effect. The results are discussed.