To address the issue of nonlinear radial distortion present in multimodal remote sensing images, this study proposes a method for matching multimodal remote sensing images that integrates phase symmetry features with rank-based local self-similarity. Initially, the local phase information of the images is utilized to construct a phase symmetry map, upon which feature extraction is performed using the features from the accelerated segment test (FAST) algorithm. Subsequently, a new feature descriptor named RPCLSS is constructed, which combines rank-based local self-similarity and phase congruency. Finally, the fast sample consensus (FSC) algorithm is employed to eliminate mismatched points. Comparative experiments are conducted on publicly available multi-source remote sensing image datasets, comparing the proposed method against five existing advanced matching methods. The results reveal that the proposed method outperforms these state-of-the-art methods in terms of the number of correct matching points, matching precision, and matching correctness.