Theoretical studies of spin-Hamiltonian (SH) parameters associated with Pr 4+ in Sr2CeO4 single crystals have been made by using the complete diagonalizing energy matrix method (CDM) for the 4f 1 electronic configuration. The calculated results are in excellent agreement with the experimental data. The negative signs of the anisotropic gi-factors and hyperfine structure constants Ai (where i = || or ⊥ ) for the orthorhombic Pr 4+ ion in Sr2CeO4 are suggested from the calculations. By comparing the results obtained by the CDM with the experimental data, one finds it is valid to interpret the SH parameters for 4f 1 ions in crystals. The results are discussed.