The completely diagonalized Hamiltonian matrixes of order 120 of 3d3/3d7 ions configuration in the trigonal symmetry have been established by irreducible representation method and group theory, taking into account spin-orbit interaction and spin-spin interaction. The ground-state energy levels, the zero-splitting parameter and Jahn-Teller effect of ruby crystal were calculated with the matrixes. The contributions of spin doublets for the ground-state energy levels were studied. The results show that the contributions of doublets cannot be neglected. The values of theoretical calculation conform with the experiments. On this basis, the influence of spin-spin interaction on the fine structure and zero-field splitting parameter of ruby crystal was further studied, and we found that the influence of spin-spin interaction on the zero-field splitting cannot be neglected.