The formation of CO through the radiative association of the carbon (C, 2s
22p
2
3P) and oxygen (O, 2s
22p
4
3P) atoms is investigated. The corresponding cross sections and rate coefficients for temperatures T = 10–10,000 K are calculated using the quantum-mechanical approach based on ab initio potential energy curves, permanent dipole moments, and transition dipole moments, which are obtained by the internally contracted multi-reference configuration interaction method with the Davidson correction and aug-cc-pwCV5Z-DK basis set. All dipole-allowed transitions between singlet, triplet, and quintet states converging to the C (2s
22p
2
3P) + O (2s
22p
4
3P) dissociation limit are considered. Compared to the previous results that only contain the X1Σ+ → X1Σ+, A1Π → X1Σ+, and B1Σ+ → X1Σ+ transitions, our results suggest that the a′3Σ+ → a3Π and d3Δ → a3Π transitions make significant contributions to the radiative association for T = 10–30 K. The total rate coefficient at low temperatures is estimated to be about 10−18 cm3 s−1, which shows significant deviation from the previous results, where only three transitions were considered. New rate coefficients may improve the chemical modeling of CO in the low-density region of the interstellar medium.