This work presents derivation, implementation, and the first applications of the restricted-unrestricted approach based on restricted Kohn-Sham formalism for evaluation of hyperfine coupling constants. By using the spin-restricted Kohn-Sham method the well-known spin contamination problem existing in the unrestricted Kohn-Sham formalism is avoided and a proper description of spin polarization is achieved via the restricted-unrestricted approach without introducing spin contamination into the evaluation of the hyperfine coupling constants. The performance of the proposed formalism is evaluated for a set of organic radicals and transition metal compounds. The results of this investigation indicate promising accuracy of the restricted-unrestricted approach for calculation of the isotropic hyperfine coupling constants in organic radicals as well as transition metal compounds. (C) 2004 American Institute of Physics.