Traditional methods of infrared and visible image fusion generally possess disadvantages of low contrast, inconspicuous thermal infrared target, and insufficient details and textures. To address these problems, an infrared and visible image fusion method based on multiscale low-rank decomposition was proposed in this study. First, multiscale low-rank decomposition was used to decompose the infrared and visible images into multilevel local parts (saliency parts) and global low-rank parts, respectively. Second, optimal fusion rules were designed to effectively integrate the complementary information of infrared and visible images by comprehensively analyzing the characteristics of decomposed images. Finally, the fusion of the images was reconstructed according to the proposed fusion rules. The proposed fusion method was tested and verified using an open dataset. Experimental results show that the proposed method can obtain fusion images with clear targets and rich details. Further, it produced an enhanced visual effect and higher accuracy compared with other state-of-the-art fusion methods.