Hyperspectral images (HSI) have high-dimensional and complex spectral characteristics, with dozens or even hundreds of bands covering the same area of pixels. The rich information of the ground objects makes hyperspectral images widely used in satellite remote sensing. Due to the limitations of remote sensing satellite sensors, hyperspectral images suffer from insufficient spatial resolution. Therefore, utilizing software algorithms to improve the spatial resolution of hyperspectral images has become an urgent problem that needs to be solved. The spatial information and spectral information of hyperspectral images are strongly correlated. If only the spatial resolution is improved, it often damages the spectral information. Inspired by the high correlation between spectral information in adjacent spectral bands of hyperspectral images, a hybrid convolution and spectral symmetry preservation network has been proposed for hyperspectral super-resolution reconstruction. This includes a model to integrate information from neighboring spectral bands to supplement target band feature information. The proposed model introduces flexible spatial-spectral symmetric 3D convolution in the network structure to extract low-resolution and neighboring band features. At the same time, a combination of deformable convolution and attention mechanisms is used to extract information from low-resolution bands. Finally, multiple bands are fused in the reconstruction module, and the high-resolution hyperspectral image containing global information is obtained by Fourier transform upsampling. Experiments were conducted on the indoor hyperspectral image dataset CAVE, the airborne hyperspectral dataset Pavia Center, and Chikusei. In the X2 super-resolution task, the PSNR values achieved on the CAVE, Pavia Center, and Chikusei datasets were 46.335, 36.321, and 46.310, respectively. In the X4 super-resolution task, the PSNR values achieved on the CAVE, Pavia Center, and Chikusei datasets were 41.218, 30.377, and 38.365, respectively. The results show that our method outperforms many advanced algorithms in objective indicators such as PSNR and SSIM while maintaining the spectral characteristics of hyperspectral images.