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Medical image fusion mainly focuses on finding better method on combining multi-modal medical images with different characteristics, and which has been playing a significant role on clinical diagnosis and disease treatment. For the fusion of MRI (Magnetic Resonance Imaging) and CT (Computed Tomography), a novel algorithm is proposed in this paper based on LatentLRR (Latent Low Rank Representation) and gradient transfer. LatentLRR is a meaningful tool for separating out detailed information and saliency information. In order to produce saliency information fused result, image statics is used through the corresponding detailed information. For detailed information, it is separated into high frequency parts and low frequency parts by NSCT (Non-Subsampled Contourlet Transform), the former are fused by the method of scale based, and the latter are merged by local energy maxima. To obtain the reconstructed image, it needs to integrate high frequency fused parts and low frequency fused parts into one image by inverse NSCT. Finally, the final image can be given by combining the reconstructed images and saliency information fused result into one image, and for a better visual effect, optimize the final result by gradient transfer. Compared with the state-of-the-art methods on the experiments of ten pair clinical medical images MRI/CT, the proposed algorithm receives a comprehensive advantage in preserving the detailed and gradient information, not only in visual effects but also in objective evaluation. [ABSTRACT FROM AUTHOR]