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In Geosynchronous (GEO) Synthetic Aperture Radar (SAR), the linear trajectory model fits the actual slant range history in a poor approximation. For example, when the satellite passes the apogee, the velocity and squint angle based on the linear trajectory model will be imaginary numbers; when the satellite passes the perigee and equator, the linear trajectory model can cause large phase error such as hundreds of radians. Therefore, the classical chirp scaling (CS) algorithm under the linear trajectory model is not useable in GEO SAR. In this paper, an improved CS algorithm is proposed to solve the imaging in GEO SAR. Firstly, the true slant histories (curved trajectory) are accurately modeled based on vector expression. Then, an accurate Two-Dimension spectrum in GEO SAR is obtained for the first time based on the high order Taylor expansion and series reversion method. The new CS factor, range migration factor, chirp frequency rate, range and azimuth compression functions are all analytically derived over again in sequence. Finally, the simulation results show that the improved CS algorithm can realize the focusing of large scene and long synthetic aperture time (hundreds of seconds) in GEO SAR.