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To solve the problems of low image contrast and low feature representation in infrared and visible image fusion, an image fusion algorithm based on latent low-rank representation (LatLRR) and non-subsampled shearlet transform (NSST) methods is proposed. First, infrared and visible images are decomposed into base subbands, saliency subbands and sparse noise subbands by the LatLRR model. Then, the base subbands are decomposed into low-frequency and high-frequency coefficients by NSST, and a feature extraction algorithm based on VGGNet and a logical weighting algorithm based on filtering are proposed to merge the coefficients. An adaptive threshold algorithm based on the regional energy ratio is proposed to fuse the saliency subbands. Finally, the fused base subbands are reconstructed, the sparse noise subbands are discarded, and a fused image is obtained by combining the subband information after fusion. Experimental results show that for the fused image produced, the algorithm performs well in both subjective and objective evaluation.