In order to study the local structure distortion and spin-Hamiltonian parameters of Al2O3:V3+ crystal, a new model has been proposed. On the basis of it, the relationship between the crystal structure parameters and spin-Hamiltonian (SH) parameters is established using Newman crystal-field superposition model. the lattice distortion and SH parameters of Al2O3:V3+ crystal, taking into account the slight magnetic interactions, including spin-spin, spin-other-orbit and orbit-orbit interactions, have been studied using the complete diagonalization method. The calculated results are in good agreement with experimental ones. It is found that the distance between upper and lower ligand oxygen plane increases by 0.0060 nm when V3+ is doped into Al2O3 crystal. Based on the local structure distortion model, at the same time, the microscopic origins of the SH parameters have been investigated for 3d2 ions in trigonal-symmetry crystal field. The results show that the SH parameters are mainly depend on spin triplets, and the contributions to SH parameters from slight magnetic interactions are related to spin triplets only.