The narrow spectral bands of hyperspectral images (HSI) provide rich information for many visual tasks, but also pose challenges for feature extraction. Despite various deep learning methods proposed by researchers, the advantages of these architectures are not fully combined. Therefore, this study proposes a high-frequency enhanced dual-branch hyperspectral image super-resolution network (HFEDB-Net) that effectively extracts spatial and spectral information of HSI by integrating the image spatial feature extraction advantage of convolutional neural network (CNN) with the adaptive capability and long-distance dependency extraction advantage of Transformers. HFEDB-Net consists of a high-frequency information enhancement branch and a backbone branch. In the high-frequency information enhancement branch, the high-frequency information of low-resolution and high-resolution HSI is extracted by using Laplacian pyramids, and the results serve as the input and label for the high-frequency branch. A spectral-enhanced Transformer is employed as the feature extraction method for this branch. In the backbone branch, a CNN with channel attention is utilized to extract spatial features and spectral information comprehensively. Finally, the results from both branches are combined through CNN to obtain the final reconstructed image. Additionally, the attention mechanism and encoder layers of the Transformer are respectively improved by using multi-head attention and multi-scale strategies to better extract spatial and spectral information from HSI. Experimental results demonstrate that HFEDB-Net outperforms current state-of-the-art methods in terms of quantitative evaluation metrics and visual effects on two public datasets.