A new fusion method based on a dual-stage attention mechanism (DSAM) and invertible transformation was proposed aiming at the problem that existing medical image fusion methods suffer from the loss of global information, insufficient complementary information integration, and poor contrast and clarity of fused images. A DSAM was introduced into the low-frequency and high-frequency branches after wavelet decomposition in order to enhance shallow global features and deep local features, respectively. An IBRC Block was employed to achieve bidirectional and invertible integration of complementary information. A multi-modal feature weighted fusion unit (MM_FWFU) was used to complete feature aggregation. An edge detail enhancement network (EDEN) was applied to improve the detail clarity and edge contrast of the fused images. The experimental results demonstrated that the proposed method achieved improvements of 1.99%, 13.75%, 0.34% and 0.10% in standard deviation (SD), average gradient (AG), correlation coefficient (CC) and multi-scale structural similarity index measure (MS-SSIM), respectively, compared with the best-performing results among nine state-of-the-art methods. The proposed method effectively preserved deep local features from the source images, producing fused images with clear contours, high contrast and rich detail information, and exhibited strong generalization capability.