Relations between the spin-Hamiltonian (SH) parameters including the second-order zero-field splitting (ZFS) parameter D, the fourth-order ZFS parameter (a-F), the Zeeman g-factors: g//, g, g(=g//-g) and the structural parameters of ZnGa2O4:Fe3+ crystals have been established by means of the microscopic spin Hamiltonian theory and Newman's crystal field (CF) superposition model. On the basis of this, the SH parameters for Fe3+ magnetic ions in ZnGa2O4:Fe3+ crystals are investigated theoretically using the CFA/MSH (crystal field analysis/microscopic spin-Hamiltonian) software based on the full configuration complete diagonalization method. It is found that the theoretically calculated parameters including the ZFS parameters D, (a-F), and the Zeeman g-factors: g//, g, g(=g//-g) for ZnGa2O4:Fe3 + crystals are in good agreement with experimental data when taking into account the lattice distortions: R=0.0487 nm and =0.192. This investigation reveals that there is a slight local structure distortion due to Fe3 + ions in ZnGa2O4:Fe3+ crystals, but the site of Fe3+ still retains D3d symmetry. On the other hand, it is found for Fe3+ ions in ZnGa2O4:Fe3+ crystals that the contribution to the SH parameters from the spin-orbit (SO) mechanism is the most important one, whereas the contributions to the SH parameters from other four mechanisms, including the spin-spin (SS), spin-other-orbit (SOO), orbit-orbit (OO), and SO-SS-SOO-OO mechanisms, are small.