TanSat is the 1st Chinese carbon dioxide (CO2) measurement satellite, launched in 2016. In this study, the University of Leicester Full Physics (UoL-FP) algorithm is implemented for TanSat nadir mode XCO2 retrievals. We develop a spectrum correction method to reduce the retrieval errors by the online fitting of an 8th order Fourier series. The spectrum-correction model and its a priori parameters are developed by analyzing the solar calibration measurement. This correction provides a significant improvement to the O2 A band retrieval. Accordingly, we extend the previous TanSat single CO2 weak band retrieval to a combined O2 A and CO2 weak band retrieval. A Genetic Algorithm (GA) has been applied to determine the threshold values of post-screening filters. In total, 18.3% of the retrieved data is identified as high quality compared to the original measurements. The same quality control parameters have been used in a footprint independent multiple linear regression bias correction due to the strong correlation with the XCO2 retrieval error. Twenty sites of the Total Column Carbon Observing Network (TCCON) have been selected to validate our new approach for the TanSat XCO2 retrieval. We show that our new approach produces a significant improvement on the XCO2 retrieval accuracy and precision when compared to TCCON with an average bias and RMSE of ���0.08��ppm and 1.47��ppm, respectively. The methods used in this study can help to improve the XCO2 retrieval from TanSat and subsequently the Level-2 data production, and hence will be applied in the TanSat operational XCO2 processing.