The EPR g factors g// and g and the hyperfine structure constants for one substitutional Cu2+ center in CdS are theoretically investigated from the perturbation formulas of these parameters for a 3d9 ion under trigonally distorted tetrahedra. In view of the significant covalency of the [CuS4]6 cluster, the ligand contributions are taken into account on the basis of the cluster approach. According to the calculations, the impurity Cu2+ is found not to occupy exactly the ideal Cd2+ site but to suffer a small inward displacement 0.12 Å toward the ligand triangle along C3 axis. The theoretical results by considering the above impurity displacement show reasonable agreement with the experimental data. The defect structure of this Cu2+ center is also discussed.