Significant nonlinear radiation differences exist between infrared and visible images, resulting in low accuracy and poor robustness in traditional registration algorithms. To address this issue, a robust registration algorithm combining phase and edge features was proposed. To improve the accuracy of feature points, a phase-consistent superimposed moment map was established, and feature points were uniformly extracted from this map. Due to the limited descriptive power of descriptors derived from a single feature source, a descriptor combining both phase and edge features was constructed. Phase features were extracted based on a multiscale maximum index map, while edge features were extracted from the superimposed moment map. For registration, feature matching is performed to obtain the transformation relationship between the images. Experiments demonstrate that the proposed algorithm significantly improves the number of correct matching points, the correct matching rate, and overall accuracy compared to other methods.