Overtone absorption lines of 12C^16O^2 have been examined by using a tunable diode laser (TDL) spectrometer in the region around 12770 cm^-1. The spectrometer sources are commercially available double heterostructure InGaAlAs TDLs operating in "free-running" mode, which allowed the detection of the line positions within 0.01 cm^-1. The observed carbon dioxide absorption lines belong to the v1+5v3 ro-vibrational band with rotational quantum number J up to 48. The minimum absorbance detected by the spectrometer (~5x10^-6) permitted to observe the weakest lines having the absorption cross section of the order of ~1x10^-27 cm^2/molecule.