Geometric positioning accuracy is an important technical indicator for Synthetic Aperture Radar (SAR) in the geomatics domain. Airborne SAR is an important trend in SAR technology due to its advantages of high flexibility, high resolution, and low cost. Motion error and undulating terrain are the major sources of airborne SAR geometric positioning. In this paper, we consider the SAR imaging principle and imaging geometry to carefully examine the mechanism of geometric positioning error caused by the coupling of motion error and terrain fluctuation. Therefore, we propose a fast geometric precision correction method and verify the validity and effectiveness of the proposed method based on simulation results and experimental data.