We describe a method for removing systematic biases of column-averaged dry air mole fractions of CO2 (XCO2) and CH4 (XCH4) derived from short-wavelength infrared (SWIR) spectra of the Greenhouse gases Observing SATellite (GOSAT). We conduct correlation analyses between the GOSAT biases and simultaneously retrieved auxiliary parameters. We use these correlations to bias correct the GOSAT data, removing these spurious correlations. Data from the Total Carbon Column Observing Network (TCCON) were used as reference values for this regression analysis. To evaluate the effectiveness of this correction method, the tnzuncorrected/corrected GOSAT data were compared to independent XCO2 and XCH4 data derived from aircraft measurements taken for the Comprehensive Observation Network for TRace gases by AIrLiner (CONTRAIL) project, the National Oceanic and Atmospheric Administration (NOAA), the US Department of Energy (DOE), the National Institute for Environmental Studies (NIES), the Japan Meteorological Agency (JMA), the HIAPER Pole-to-Pole observations (HIPPO) program, and the GOSAT validation aircraft observation campaign over Japan. These comparisons demonstrate that the empirically derived bias correction improves the agreement between GOSAT XCO2/XCH4 and the aircraft data. Finally, we present spatial distributions and temporal variations of the derived GOSAT biases.