In order to overcomes the problems of fusion image details loss, edge blur, lack of contrast and clarity existing in the existing fusion algorithms, an infrared and visible image fusion algorithm based on dynamic range compression enhancement and the non-subsampled shearlet transform is proposed. Fully retain details and edge information of infrared and visible images. Firstly, the weak visible image is enhanced by the high dynamic range compression enhancement method, and the visible image with good brightness and contrast is obtained. Secondly, the infrared and visible images are decomposed by the non-subsampled shearlet transform, and the corresponding low-frequency and high-frequency coefficients are obtained. Then, the high-frequency coefficients are reduced by the hard threshold shrinkage to suppress the noise in the high frequency coefficients. The average fusion method based on visual-saliency-map weighting and the fusion method based on large absolute value are used to fuse the low-frequency and high-frequency coefficients respectively. Finally, the fused image is reconstructed by the inverse non-subsampled shearlet transform. In order to evaluate the algorithm objectively, spatial frequency, information entropy, edge intensity, average gradient, noise variance and natural image quality evaluation are used as image quality evaluation indexes. To verify the effectiveness of the proposed algorithm, feasibility verification experiment, parameter analysis experiment and performance comparison experiment were carried out respectively. The feasibility verification experimental results show that the spatial frequency, edge information and average gradient of the fused images are significantly improved compared with the original infrared and visible images, which shows that the proposed algorithm can effectively improve the contrast and clarity of the image, and has a good edge preservation ability. At the same time, the information entropy of the fused images and the original infrared and visible images have little difference, which indicates that the proposed algorithm can protect the details of the original image well. In the parameter analysis experiment, to analyze the influence of the selection of threshold shrinkage proportion coefficient on the quality of the fused image, subjective visual analysis and objective data analysis were carried out on the test results under different parameter combinations, and a group of better threshold shrinkage proportion coefficient was obtained. In the performance verification experiment, the fusion performance of the proposed fusion algorithm and other seven comparison algorithms is compared from subjective and objective aspects. Compared with the other seven algorithms, the proposed algorithm has bright background, high contrast, intact edge details, and better overall visibility of the fused image. It has advantages in spatial frequency, edge information, information entropy and average gradient, among which the advantages of spatial frequency, edge information and average gradient are more prominent, indicating that the proposed algorithm has better performance in texture detail expression, edge detail feature retention and visual clarity. To further verify the efficiency of the algorithm, 10 groups of infrared and visible images with the size of 270×360 were selected, and the average time of each group of images was obtained. The operating efficiency of the proposed algorithm is better than that of the other two comparison algorithms based on the non-subsampled shearlet transform decomposition, but lower than that of DTCWT, WLS-VSM and TE-MST. In order to verify the noise reduction effect of the proposed algorithm, Gaussian noise with variance of 5 and 10 is added to the test image respectively to form the noise test image. Eight algorithms are used to fuse the two groups of noise images respectively. Compared with the other 7 algorithms, the noise variance index of the fused image obtained by the proposed algorithm is the smallest, which indicates that its noise suppression effect is better. Experimental results show that this algorithm can fuse infrared and visible images effectively, which cannot be achieved by a single type of image, and thus improve the image identification reliably. Compared with existing fusion algorithms, this algorithm has certain advantages in detail information retention, contrast enhancement and edge blur suppression.