The energies,equilibrium geometries and harmonic frequencies of the ground state X³Σ_g^- and the first excited state A³Σ_u^- of a B₂ molecule are calculated using the GSUM(Group Sum of Operators) method of SAC/SAC-CI with the basic sets(D95(d),) 6-311g^** and cc-PVTZ.It is found that the basis set D95(d) is suitable for the energy calculation of a B₂ molecule.The potential curves are scanned using the SAC/D95(d) method for the ground state and the SAC-CI/D95(d) methods for the excited states.A least square is fitted to a Murrell-Sorbie function.The spectroscopy constants(B_e,α_e,ω_e,and ω_eχ_e) are calculated which are in good agreement with experiment.It is believed that the Murrell-Sorbie function and the SAC/SAC-CI method are suitable not only for the ground state,but also for low-lying excited states.