The work aims to propose a color image fusion algorithm based on multistage low-rank representation and HSI color space, so as to improve the visibility of infrared and color visible fusion images, and reproduce the contrast and color effect of images better. Firstly, the RGB image of color visible light was converted into HSI color space through the conversion of RGB to HSI color space and the H, S and I channels were separated. Then, LatLRR was used to decompose the channel-I image of the color visible image and the infrared image at the second stage to obtain the details and basic parts. The details of channel I and infrared image were fused with the nuclear norm adaptive weighted fusion strategy, and the basic parts were fused with the fuzzy logic value adaptive weighted fusion strategy. Finally, the fused details and basic parts were added together to produce a new channel-I image, which was combined with H and S channels and then transferred to RGB color space to obtain the fusion image. The fusion image obtained by the algorithm had the smallest subjective color distortion, the clearest scene details and the more prominent infrared target. Meanwhile, the objective evaluation index value increases by about 1%~24%. The proposed algorithm is effective and can improve the result of color image fusion.