The spin Hamiltonian parameters (g factor and hyperfine structure constants) of Cr+ in ZnX (X = S, Se, Te) and CdTe are theoretically investigated, using the perturbation formulas of these parameters for a tetrahedral 3d5 cluster. Both the contributions from the crystal-field (CF) and charge transfer (CT) mechanisms are considered from the cluster approach. The calculated results show good agreement with the experimental data. The CT contribution to g-shift Δg (=g − gs, where gs =2.0023 is the spin only value) is opposite (positive) in sign related to the CF one, and its importance (characterized by the relative ratio (|ΔgCT/ΔgCF|) is 11%, 66% and 104% (71%) for ZnS, ZnSe and ZnTe (CdTe), respectively. ACT from the CT contribution to hyperfine structure constant is the same (positive) in sign and about 50–53% in magnitude as compared with ACF from the CF one.