The positioning accuracy of synthetic aperture radar (SAR) images is affected by factors, such as satellite platform instability, aging of on-board instruments, and environmental changes. Geometric calibration is a commonly employed and cost-effective method to enhance the positioning accuracy of SAR images. The classical point-based geometric calibration (PB-GC) model, however, only utilizes the location of ground control points (GCPs) and does not fully exploit the spatial relationships among the GCPs. This study introduces a high-precision geometric calibration method that builds upon the classical model for calibrating SAR imaging systems. This method incorporates the Co-Line-GC and Co-Circle-GC models, where the former uses GCPs distributed on a line while the latter uses GCPs distributed on a circle. The results reveal that, compared to the classical model, our approach enhances the positioning accuracy of Gaofen-3 and Sentinel-1A SAR images by approximately 2 m in eastern China, achieving a mean positioning accuracy of 3.02 m. In terms of calibration performance, a comparison between postcalibrated and precalibrated images indicates that the images are shifted, not distorted, and a better match of the same features between different scenes in the image mosaic is observed after calibration. The improved positioning accuracy of SAR images significantly contributes to global remote sensing mapping, land use change monitoring, and ground target detection applications.