Multimodal medical image fusion can combine salient information from different source images of the same part and reduce the redundancy of information. In this paper, an efficient hybrid image decomposition (HID) method is proposed. It combines the advantages of spatial domain and transform domain methods and breaks through the limitations of the algorithms based on single category features. The accurate separation of base layer and texture details is conducive to the better effect of the fusion rules. First, the source anatomical images are decomposed into a series of high frequencies and a low frequency via nonsubsampled shearlet transform (NSST). Second, the low frequency is further decomposed using the designed optimization model based on structural similarity and structure tensor to get an energy texture layer and a base layer. Then, the modified choosing maximum (MCM) is designed to fuse base layers. The sum of modified Laplacian (SML) is used to fuse high frequencies and energy texture layers. Finally, the fused low frequency can be obtained by adding fused energy texture layer and base layer. And the fused image is reconstructed by the inverse NSST. The superiority of the proposed method is verified by amounts of experiments on 50 pairs of magnetic resonance imaging (MRI) images and computed tomography (CT) images and others, and compared with 12 state-of-the-art medical image fusion methods. It is demonstrated that the proposed hybrid decomposition model has a better ability to extract texture information than conventional ones.