The total partition function was calculated for carbon monoxide with approximation. Using the dipole moment function and the wave function with Morse approximation, we computed the matrix elements of vibrational-rotational transition and absorption coefficient at normal and high temperature. The computed results agreed with the HITRAN database and literature, which shows that the calculation of total partition function and matrix elements of vibrational-rotational transition is reliable. Furthermore, the absorption coefficient and radiant spectrum are also presented at higher temperature of 4 000 and 6 000 K.