The potential energy curves (PECs) are calculated for the 20 Λ-S states (X2Πg, A2Πu, B2Σ−g, a4Πu, b4Σ−g, b′4Πg, c4Σ−u, 12Σ+g, 12Σ+u, 12Σ−u, 14Σ+g, 14Σ+u, 14Δg, 14Δu, 16Σ+g, 16Σ+u, 16Πg, 16Πu, 24Πg and 24Πu) of O2+ cation and their corresponding 58 Ω states. Of these 20 Λ-S states, the 16Πu state is found to be repulsive. The 12Σ+g, 14Σ+u, c4Σ−u and 14Δu states are found to possess the double well. The b4Σ−g, 16Σ+g, 14Σ+u, a4Πu, A2Πu, 16Πg and 24Πg states are found to be inverted with the spin–orbit coupling effect included. The b′4Πg, 16Πg, 16Σ+g, 14Σ+u and 14Δu states, and the second well of the 12Σ+g state are found to be the weakly bound states. The b′4Πg state is found to possess one well with one barrier. The PECs are calculated by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson correction in combination with the aug-cc-pV6Z basis set. The core–valence correlation and scalar relativistic corrections are included. The convergent behaviour of present calculations is discussed with respect to the basis set and theoretical level. The spin–orbit coupling effect is accounted for. The PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated, and compared with available measurements. It demonstrates that the spectroscopic parameters reported here can be expected to be reliably predicted ones.