Subsurface structural distribution can be detected using Ground-Penetrating Radar (GPR). The distribution can be considered as road fingerprints for vehicle positioning. Similar to the principle of visual image matching for localization, the position coordinates of the vehicle can be calculated by matching real-time GPR images with pre-constructed reference GPR images. However, GPR images, due to their low resolution, cannot extract well-defined geometric features such as corners and lines. Thus, traditional visual image processing algorithms perform inadequately when applied to GPR image matching. To address this issue, this paper innovatively proposes a GPR image matching and localization method based on a novel feature descriptor, termed as central dense structure context (CDSC) features. The algorithm utilizes the strip-like elements in GPR images to improve the accuracy of GPR image matching. First, a CDSC feature descriptor is designed. By applying threshold segmentation and extremum point extraction to the GPR image, stratified strip-like elements and pseudo-corner points are obtained. The pseudo-corner points are treated as the centers, and the surrounding strip-like elements are described in context to form the GPR feature descriptors. Then, based on the feature description method, feature descriptors for both the real-time image and the reference image are calculated separately. By searching for the nearest matching point pairs and removing erroneous pairs, GPR image matching and localization are achieved. The proposed algorithm was evaluated on datasets collected from urban roads and railway tracks, achieving localization errors of 0.06 m (RMSE) and 1.22 m (RMSE), respectively. Compared to the traditional Speeded Up Robust Features (SURF) visual image matching algorithm, localization errors were reduced by 86.6% and 95.7% in urban road and railway track scenarios, respectively.