Remote sensing hyperspectral image single super-resolution (HSISR) tasks have made considerable progress in recent years. Methods using deep convolutional neural network (CNN) technology are widely employed. However, most CNN-based super-resolution models tend to ignore the spectral structure of remote sensing hyperspectral images. Meanwhile, due to the limitation of convolutional networks by the size of convolutional kernels, long-distance feature dependencies are ignored, which in turn affects the reconstruction accuracy. To solve these problems, this study proposes adual-branch remote sensing hyperspectral image super-resolution network based on grouped ConvLSTM and Transformer (DGCTNet), which combines the advantages of Transformer in capturing long-distance dependencies and ConvLSTM in extracting sequential features. It enhances the reconstructed image effect by extracting spatial features while maintaining spectral orderliness. In addition, DGCTNet also designs an edge learning network to diffuse edge information into the image space. At the same time, to recalibrate the spectral response, the proposed dual-group level channel self-attention mechanism (DSA) is added. Experiments on the Houston dataset show that the proposed DGCTNet method outperforms the current state-of-the-art comparison models in terms of quantitative evaluation metrics and visual quality in a wide variety of scenarios.