A super-resolution method based on matching extraction and a cross-scale feature fusion network is proposed to address the problem that the spatial resolution of the FY-4 satellite image's near-infrared and short-wave infrared bands is far lower than the corresponding visible band. The high-resolution band image is used as the reference image to assist in the reconstruction of the low-resolution visible and near-infrared bands. First, using the similarity between the high-resolution image and the low-resolution image, the matching extraction module is used to fuse the fine texture information of the high-resolution image into the low-resolution image. The cross-scale feature fusion method is then used to combine the reference image feature map and the low-resolution feature map, which still differ in brightness, color, structure, and so on. Finally, by combining the total spatial spectral variation loss and the L1 loss, the spatial and spectral reliability of the reconstruction results is ensured. Experimental results demonstrate that the proposed method achieves good results in spatial and spectral reliability. This method achieves the best quality evaluation index and can effectively improve the spatial resolution of FY-4 satellite images compared with Bicubic, RDN, RCAN, EDSR, Dsen2, and other methods.