In this paper, we propose a deep residual spatial attention network (DRSAN) for hyperspectral (HS) pansharpening. Different from the existing methods, our newly proposed method not only considers the spatial information of both the panchromatic (PAN) and the HS image simultaneously, but also adaptively learns more informative features of spatial locations for details enhancement, which mainly includes four steps. Firstly, the spatial details of the enhanced PAN image are obtained through the structure tensor. Then we extract the spatial information of the upsampled HSI by using the guided filter. The integrated spatial information of both PAN and HS images is subsequently fed into the DRSAN to map the residual HSI between the upsampled HSI and the reference HSI, where several residual spatial attention blocks (RSABs) are cascaded to exploit more useful details information. Finally, the fused HSI is generated by the summation of the upsampled HSI and the reconstructed residual HSI. Extensive visual and quantitative assessments validate the superiority of our proposed DRSAN over the state-of-the-art HS pansharpening methods.