The potential energy curves (PECs) of eight low-lying electronic states (X1Σ+, a3Π, a′3Σ+, d3Δ, e3Σ−, A1Π, I1Σ−, and D1Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self-consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation-consistent aug-cc-pV5Z basis set. The effects on the PECs by the core-valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third-order Douglas–Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. Core-valence correlation corrections are performed using the cc-pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (De, Te, Re, ωe, ωexe, ωeye, Be, αe, and γe) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a3Π electronic state. With the PECs obtained by the MRCI+Q/aug-cc-pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant Bν, and centrifugal distortion constant Dν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug-cc-pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.