When SAR raw data is being focused, a linear phase term was introduced in azimuth lines of focused image, due to the nonzero Doppler centroid generated by the earth rotation and the SAR sensor positioning disturbances. Therefore, we can not resample the azimuth lines as baseband signal during interferometric processing. Generally, in order to keep the integrity of the phase information, a azimuth interpolation kernel spectrum is shifted to Doppler centroid. Because of the specialty of sliding spotlight imaging mode, the Doppler centroid is distributed more complex, and azimuth lines become time-varying signal. In this paper, the Doppler change history and the change rule of Doppler centroid of azimuth lines based on sliding spotlight mode imaging theory, and time-varying signal interpolation method is analyzed. Also, the interpolation accuracy affected by nonzero Doppler centroid is discussed based on simulation experiment. Then, an improvement in resample process chain of Delft-DORRIS is introduced, which is implemented by shifting interpolation kernel in azimuth according to the new Doppler centroid equation. Finally an imagine focus processing of sliding spotlight mode image from TerraSAR-X satellite is produced by the new resample process chain.