In geosynchronous synthetic aperture radar (GEO SAR), owing to the increase of signal propagation delay time and synthetic aperture time, the straight track approximation is inadequate. Most formulations and imaging algorithms based on the conventional hyperbolic range equation (CHRE) are not proper for GEO SAR directly. Thus, we tentatively aim to present an advanced range equation in this paper. The proposed equation is a fourth-order equation, which can improve the accuracy in the approximation of the range history for GEO SAR. Furthermore, the accurate two dimensional (2-D) frequency spectrum (PTFS) expression of a point target is obtained by the method of series reversion (MSR). It is found that the corresponding range cell migration correction (RCMC) reference function must be considered higher order term than the standard RD algorithm. Therefore, the modified Range Doppler (RD) algorithm is proposed based on the new spectrum. The simulation results validate the precision and efficiency of the improved range equation and the algorithm. (4 pages)