In this paper, a near-infrared laser heterodyne spectrometer developed by the laboratory is used to investigate the inversion of greenhouse gas column concentration and approximately evaluate the system measurement errors based on the optimal estimation algorithm. Firstly, the spectral database and the calculation results from the reference forward model are compared with the ground-based FTIR results, thereby selecting the detection window, the corresponding laser and detector. Secondly, the optimal estimation concentration inversion algorithm based on the reference forward model is established, and the Levenberg-Marquardt (LM) iterative method is adopted to realize the inversion of the concentration and vertical distribution profile of atmospheric CO₂ column in the whole layer, and the long-term observation comparative experiment is carried out to verify the feasibility of this algorithm. Finally, by simulating the selected detection window spectrum in different white noise, the approximate corresponding relationship between the system signal-noise-ratio (SNR) and CO₂ column concentration measuring error is eventually obtained. This research is an indispensable theoretical calculation part of the detection system and will conduce to improving the application of laser heterodyne technology in atmospheric observations.