Image registration is a basic step for remote sensing image processing, such as classification, change detection, and so on. Registration of unmanned aerial vehicle (UAV) images is a challenging task because of illumination change, obvious rotation, viewpoint change, and similar textures. The change in viewing angle between adjacent images causes significant difficulties in image matching, especially for residential areas and high-rise buildings. Therefore, the feature points on the buildings are removed by morphological processing when detecting feature points in this study. Considering the similarity of terrain structural properties between adjacent UAV images, the scene shape similarity feature (SSSF) descriptor is utilized to capture the structural similarity. However, the SSSF descriptor is influenced by the illumination changes of UAV images. The phase congruency algorithm is adopted to replace the Canny operator to detect structural features when calculating the SSSF descriptors because of its robustness for illumination change. Then, the normalized correlation coefficient of SSSF descriptors is used as the similarity metric to detect tie points. Finally, the point pairs with large residuals are eliminated by random sample consensus algorithm and the tie points are detected by iteratively removing the mismatched points. The proposed method was compared to some recent related methods using correct matching ratio, root-mean-square error, and time. Five experiments including habitation, bare land, mixed terrain, farmland, and buildings are carried out to evaluate the effectiveness of the proposed method. Registration results demonstrate that the proposed method is robust for illumination and viewpoint change of UAV images and usually generates more accurate registration results than some popular registration methods.