Geosynchronous synthetic aperture radar (GEO SAR) has the characteristics of long aperture time and large imaging area. Therefore, the conventional imaging algorithm in Low Earth Orbit (LEO) SAR loses effect. In this paper, based on curved trajectory model under an ideal acquisition and not considering some acquisition perturbations (atmosphere, orbital deviations), an accurate two-dimensional frequency spectrum is analytically obtained via series reversion principle and high order Taylor expansion. Then, an improved Nonlinear Chirp Scaling (NCS) algorithm is proposed in GEO SAR, which includes novel range migration correction factor, coupling phase compensation factor, NCS factor and azimuth compression function. Finally, the correctness of the proposed NCS algorithm is verified via imaging results of point array targets and area targets.