[en] The spin-Hamiltonian parameters (g factors g_||, g_{perpendicular} and hyperfine structure constants ¹⁶¹A_||, ¹⁶¹A_{perpendicular}, ¹⁶³A_||, ¹⁶³A_{perpendicular}) for Dy³⁺ at the tetragonal H_f⁴⁺ site of H_fSiO₄ crystal are calculated from the diagonalization (of energy matrix) method. In the method, we add the Zeeman (or magnetic) and hyperfine interaction terms to the conventional Hamiltonian used in the calculations of crystal-field energy levels. The 66x66 energy matrix concerning the new Hamiltonian is established by considering the ground multiplet ⁶H_15/2 and the first to fifth excited multiplets ⁶H_J (where J=13/2, 11/2, 9/2, 7/2 and 5/2), and the crystal-field parameters in the energy matrix are calculated from the superposition model. From the calculations, the spin-Hamiltonian parameters of H_fSiO₄:Dy³⁺ are explained reasonably and the signs of hyperfine structure constants for ¹⁶¹Dy³⁺ and ¹⁶¹Dy³⁺ isotopes in H_fSiO₄ are suggested. The results are discussed.