The axial shift and the spin Hamiltonian parameters (zero-field splitting D, g factors and hyperfine structure constants) for Cr+ in BeO are theoretically studied in this work. The calculations are carried out by using the perturbation formulas of these parameters for a 3d5 ion under trigonally distorted tetrahedra based on the cluster approach containing both the crystal-field and charge transfer contributions. It is found that the impurity Cr+ may not occupy exactly the host Be2+ site but experience a small outward shift 0.01 Å away from the ligand triangle along the C3 axis. The above impurity axial shift leads to much smaller trigonal distortion than the host Be2+ site in BeO. The theoretical spin Hamiltonian parameters based on the above impurity axial shift are in good agreement with the observed values.