To get more obvious target information and more texture features, a new fusion method for the infrared (IR) and visible (VIS) images combining regional energy (RE) and intuitionistic fuzzy sets (IFS) is proposed, and this method can be described by several steps as follows. Firstly, the IR and VIS images are decomposed into low- and high-frequency sub-bands by non-subsampled shearlet transform (NSST). Secondly, RE-based fusion rule is used to obtain the low-frequency pre-fusion image, which allows the important target information preserved in the resulting image. Based on the pre-fusion image, the IFS-based fusion rule is introduced to achieve the final low-frequency image, which enables more important texture information transferred to the resulting image. Thirdly, the ‘max-absolute’ fusion rule is adopted to fuse high-frequency sub-bands. Finally, the fused image is reconstructed by inverse NSST. The TNO and RoadScene datasets are used to evaluate the proposed method. The simulation results demonstrate that the fused images of the proposed method have more obvious targets, higher contrast, more plentiful detailed information, and local features. Qualitative and quantitative analysis results show that the presented method is superior to the other nine advanced fusion methods.