The fusion of infrared and visible images together can fully leverage the respective advantages of each, providing a more comprehensive and richer set of information. This is applicable in various fields such as military surveillance, night navigation, environmental monitoring, etc. In this paper, a novel infrared and visible image fusion method based on sparse representation and guided filtering in Laplacian pyramid (LP) domain is introduced. The source images are decomposed into low- and high-frequency bands by the LP, respectively. Sparse representation has achieved significant effectiveness in image fusion, and it is used to process the low-frequency band; the guided filtering has excellent edge-preserving effects and can effectively maintain the spatial continuity of the high-frequency band. Therefore, guided filtering combined with the weighted sum of eight-neighborhood-based modified Laplacian (WSEML) is used to process high-frequency bands. Finally, the inverse LP transform is used to reconstruct the fused image. We conducted simulation experiments on the publicly available TNO dataset to validate the superiority of our proposed algorithm in fusing infrared and visible images. Our algorithm preserves both the thermal radiation characteristics of the infrared image and the detailed features of the visible image.