A high sensitivity and global coverage of carbon dioxide (CO₂) observation are expected to be designed as the next generation measurement by space-borne integrated path differential absorption (IPDA) lidar. Strict spatial CO₂ data, such as 1×10^-6 or better accuracy, are needed to solve the most scientific problems of carbon cycle. Spectral purity, that is, the ratio of effective absorption energy to total transmission energy, is one of the most important parameters of IPDA lidar. It directly affects the accuracy of CO₂ measurements. Due to the comparison of the average dry air mixing ratio from the two echo pulse signals, the laser output usually accompanied by an unexpected spectral broadband background radiation will produce significant systematic errors. In this study, the shape of the spectral energy density line and the shape of the spectral impurity line are modeled as the shape of the Lorenz line for simulation, and the off-line is assumed to be a CO₂ reference that is not absorbed. Based on the IPDA detection theory, the error equations for calculating the systematic errors caused by spectral impurities are derived. For spectral purity of 99%, the induction error can reach 8.97×10^-6. A narrow band filter can be used to achieve significant relaxation. The narrow band filter blocks a large amount of impurity radiation transmitted outside a certain spectral interval, ensures that the return radiation focuses on the target operating wave number and reduces the error caused by the inadequately caused. The experimental results show that for a given spectral purity, the error can be suppressed by smaller FWHM of spectral impurity and bandwidth of narrow-band filter. The results reveal that an error of 0.084×10^-6 of the retrieved CO₂ column ratio is derived from the influence of spectral impurity with the spectral purity of 99.9% and spectral impurity of 9GHz in conjunction with a narrow-band spectral filter of 1GHz FWHM and transmittance of 0.86. In addition, random error less than 0.02×10^-6 is caused by the attenuation of narrow-band filter with the laser energy of 100mJ.