Hyperspectral image produces high spectral resolution at the sacrifice of spatial resolution. Without reducing the spectral resolution, improving the resolution in the spatial domain is a very challenging problem. Motivated by the discovery that hyperspectral image exhibits high similarity between adjacent bands in a large spectral range, in this paper, we explore a new structure for hyperspectral image super-resolution (DualSR), leading to a dual-stage design, i.e., coarse stage and fine stage. In coarse stage, five bands with high similarity in a certain spectral range are divided into three groups, and the current band is guided to study the potential knowledge. Under the action of alternative spectral fusion mechanism, the coarse SR image is super-resolved in band-by-band. In order to build model from a global perspective, an enhanced back-projection method via spectral angle constraint is developed in fine stage to learn the content of spatial-spectral consistency, dramatically improving the performance gain. Extensive experiments demonstrate the effectiveness of the proposed coarse stage and fine stage. Besides, our network produces state-of-the-art results against existing works in terms of spatial reconstruction and spectral fidelity. Our code is publicly available at https://github.com/qianngli/DualSR.