In order to solve the problem that the different intensity of the same position of the 3-D positron emission tomography(PET) and the magnetic resonance imaging(MRI) image of Alzheimer’s disease and retain the MRI atrophy of the cerebral cortex, cerebral sulcus, hippocampus, etc. Two images were firstly pre-processed in SPM to obtain two images. Then, using ShearLab 3D transform to process the advantages of high-dimensional data to decompose to obtain low and high-pass subbands. The high frequency subband was divided into intermediate and high frequency subband with the variance as threshold. The fusion principle of low-pass subbands was based on the method of three-dimensional extended weighted local energy and weighted sum of modified Laplacian based on 26 neighborhoods. The sharpening operator was introduced as a weight parameter to make the edge of the fused image clear. Intermediate subband enhances the edge information with absolute value activity. The high-pass subbands were combined with three three-dimensional low-level visual features to enhance the detailed features of the image. Finally, PET/MRI fusion images were obtained using ShearLab 3D inverse transform. The results show that the fusion result of ShearLab 3D transform is better than the spatial algorithm and wavelet transform as a whole. In the ShearLab 3D method, different fusion rules are compared and analyzed. The average gradient, spatial frequency, edge strength, and comprehensive entropy of the fusion result of this algorithm were improved by 11.09%, 22.58%, 152.68%, and 0.58%, respectively. It solves the problems of blurred edges and unclear details in fusion image. This study provides a reference for PET/MRI image fusion.