Based on crystal-and ligand-field theory, double-spin-orbital coupling approach was used to analyze the crystal-field energy levels and spin-Hamiltonian parameters of Ni 2+ ion at trigonal site in CdBr 2 . The local lattice distortion (∆R and τ Ni 2+ ) is estimated from the crystal field parameters; the crystal field energy Hamiltonian was diagonalized in the full basis consisting of 45 wave functions of the Ni 2+ ion. Results of calculations are in good agreement with experimental data. The reasonableness of the theoretical results is discussed.