Large-scale electronic structure calculations were performed to generate a three-dimensional potential energy function for the X¹Σ⁺ state of C₂B^-. Spectroscopic constants and anharmonic ro-vibrational levels were calculated variationally and by perturbation theory using this function. The ground state possesses an equilibrium geometry with R_e^CC=1.270 Åand R_e^CB=1.461 Å, the fundamental vibrational transitions are predicted at ν₁^CB(J=0)=1014.7 cm^-1, ν₂(J=1)=125.4 cm^-1 and ν₃^CC(J=0)=1935.4 cm^-1 (exp. 1936.3 cm^-1). The difference electron density plot showed that the negative charge is almost entirely localized in the boron lone pair and the BC bond region. The A¹Π–XΣ⁺T_e excitation energy was calculated to be 23722 cm^-1 confirming the assignment made for the transition detected at T₀=23131 cm^-1 in a neon matrix. For the A¹Π state an equilibrium geometry with R_e^CC=1.324 Åand R_e^CB=1.396 Åwas obtained. The vertical excitation energy of the a³Π–X ¹Σ⁺ transition is predicted at 15306 cm^-1. Both excited states lie below the vertical detachment energy calculated at 25845 cm^-1.