In Multi-scale Geometric Analysis (MGA)-based fusion methods for infrared and visible images, adopting the same representation for the two types of the images will result in the non-obvious thermal radiation target in the fused image, which can hardly be distinguished from the background. To solve the problem, a novel fusion algorithm based on nonlinear enhancement and Non-Subsampled Shearlet Transform (NSST) decomposition is proposed. Firstly, NSST is used to decompose the two source images into low- and high-frequency sub-bands. Then, the Wavelet Transform (WT) is used to decompose high-frequency sub-bands into obtain approximate sub-bands and directional detail sub-bands. The “average” fusion rule is performed for fusion for approximate sub-bands. And the “max-absolute” fusion rule is performed for fusion for directional detail sub-bands. The inverse WT is used to reconstruct the high-frequency sub-bands. To highlight the thermal radiation target, we construct a non-linear transform function to determine the fusion weight of low-frequency sub-bands, and whose parameters can be further adjusted to meet different fusion requirements. Finally, the inverse NSST is used to reconstruct the fused image. The experimental results show that the proposed method can simultaneously enhance the thermal target in infrared images and preserve the texture details in visible images, and which is competitive with or even superior to the state-of-the-art fusion methods in terms of both visual and quantitative evaluations.