The spin-Hamiltonian parameters (g factors g∥ and g⊥ and zero-field splittings , , , and ) for Gd3+ ions at the tetragonal Y3+ site of YBa2Cu3O6+y (y = 0.06) superconductor are calculated together from a diagonalization (of the energy matrix) method based on the one-electron crystal field mechanism. In the method, a 56 × 56 energy matrix concerning the ground multiplet 8S7/2 and the excited multiplets 8L7/2 (where L = P, D, F, G, H, I) for 4f7 ions at a tetragonal crystal field and under an external magnetic field is constructed and used. The crystal field parameters in the energy matrix are obtained from the superposition model. The calculated results are in reasonable agreement with the experimental values. The defect structure (characterized by the angular distortion Δθ) of the Gd3+ impurity centers in YBa2Cu3O6+y is also acquired from the calculation. The results are discussed.