The spin-Hamiltonian parameters ($g$ factors $g_{||}, g{|perp}$ and hyperfine structure constants $A_{||}$, $A{|perp}$) and the local structure for the tetragonal $Cu^{2+}$ centre in trigonal $ZnGeF_{6}·6H_{2}O$ crystal are theoretically studied using the perturbation formulae of these parameters for a 3d9 ion in tetragonally elongated octahedra. In the calculations, the contributions to the spin-Hamiltonian 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, and the required crystal field parameters are obtained using the superposition model and the local structures of the studied $[Cu(H_{2}O)_{6}]^{2+}$ cluster. According to the calculations, the ligand octahedra around $Cu^{2+}$ suffer relative elongation$\tau{\sim 0.085 \AA) along the [0 0 1] (or $C_4$) axis for the tetragonal $Cu^{2+}$ centres in $ZnGeF_{6}·6H_{2}O$ crystal, due to the Jahn--Teller effect. The calculated results show good agreement with the experimental data.