To modify the geocentric core distance error of a Time Delay and Integration (TDI) CCD space camera in the calculation of image motion compensation, and decrease the influence of the error on the match error of image motion velocity, a model of image motion calculation of points bellow satellites was deduced. The influence of the geocentric core distance error on the relative error of image motion velocity was analyzed based on the model, and the geocentric core distance error was modified by two steps according to the error sources. The former adopted the World Geodetic System (WGS-84) to modify the error generated by ellipticity of the error, and the latter used the data source of the earths height above sea level (United States Geological Survey Digital Elevation Model, USGS DEM) to make a digital elevation map modify the error generated by the deference heights above sea level. After modifying, the image motion model of points bellow satellites was deduced. The calculation and analysis by the model indicate that the maximum error of image motion velocity eliminated are about 2.85% and 1.76% with the modification of geocentric core distance error by the WGS-84 model and digital elevation map,respectively. Those data clearly show that the match error of forward direction(the integral direction of TDI CCD)has been greatly decreased by modifying the geocentric core distance error, and the imaging quality of TDI CCD space camera has improved greatly.