Multi-sensor infrared and visible image fusion is to extract image features captured by multi-sensor devices to generate a fusion image that contains both infrared thermal radiation and visible texture details. Based on this purpose, this paper proposes a novel infrared and visible image fusion method via double joint edge preservation filter and non-globally saliency gradient operator. First, the source images are finely decomposed by the proposed filter, which has the merits of multi-level scale awareness and double joint edge preservation, into the base, infrared detail, and visible detail layers. Furthermore, to ensure that the overall appearance of the fused image is maximally similar to the source images, a maximum-absolute rule is introduced to process the base layers. Then, a non-globally saliency gradient operator constructed by three different kinds of basic operators is presented to dominate the fusion of the detail layers, aiming to filter out the redundant information and recover the saliency features. Finally, the merged image is obtained by summating the fused base and detail layers. The experimental results demonstrate that the proposed method not only fully extracts the visible details and infrared thermal target of the source images but also generates a fused image with excellent subjective performance and objective indicators compared to other state-of-the-art fusion methods.