High-resolution synthetic aperture radar (SAR) satellites have become an important way to observe the earth. However, the geometric positioning accuracy of SAR satellite images across different times and spaces is an important factor affecting the realization of global remote sensing applications. In this study, a multimode hybrid geometric calibration method that incorporates an atmospheric propagation delay correction and that can be used to detect systematic errors affecting the geometric positioning accuracy of SAR satellites is described. The spatiotemporal variation reasons of geometric positioning error sources for spaceborne SAR are then analyzed. Finally, the stability of geometric positioning accuracy is evaluated using the described method on data extracted from Yaogan-13 (YG-13) SAR satellite images with long time series and multiple test areas in China. The results reveal that during the study period (2015–2017), the geometric positioning accuracy of the YG-13 SAR system was relatively stable and is better than 3 m regardless of the spatial distribution, after removal of systematic pulse-dependent slant range errors and atmospheric correction. Furthermore, the validation results provide a reference for the design of SAR satellite systems, the establishment of calibration periods, and quantitative remote sensing application.