In order to solve the problems of scale difference, inconspicuous spatial feature expression, redundancy, and overlapping of spectral feature information in hyperspectral and multispectral image fusion, a fusion algorithm based on multi-scale space-spectrum hybrid attention network is designed in this paper. The algorithm enhances the capability of shallow feature extraction through the multi-scale mechanism, uses the space-spectrum hybrid attention mechanism to mine the correlation between deep space and spectrum, designs a cross-spectrum fusion module to realize the effective reconstruction of spatial and spectral information, and uses the loss function to constrain the difference between the fused image and the reference image in terms of color, detail edge, and spatial structure. Experiments were conducted on PaviaUniversity, IndianPines, and hyperspectral image of Natural Scenes2004 datasets, and compared to algorithms such as ResTFNet, spatial spectral reconstruction network, MoGDCN, DBSR, and Fusformer. The proposed algorithm, MSSSHANet, performs better in spectral curve smoothness, spectral difference value, root mean squared error, peak signal to noise ratio, Erreur Relative Globale Adimensionnelle de Synthèse, and Spectral Angle Mapper value, which plays an active role in improving fusion quality. However, the generalization ability of the proposed algorithm in special remote sensing tasks needs to be verified, and future research will focus on data preprocessing optimization and the development of time-spatial-spectral integration fusion technology.