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Pansharpening aims at fusing the rich spectral information of multispectral (MS) images and the spatial details of panchromatic (PAN) images to generate a fused image with both high resolutions. In general, the existing pansharpening methods suffer from the problems of spectral distortion and lack of spatial detail information, which might prevent the accuracy computation for ground object identification. To alleviate these problems, we propose a Hybrid Attention mechanism-based Residual Neural Network (HARNN). In the proposed network, we develop an encoder attention module in the feature extraction part to better utilize the spectral and spatial features of MS and PAN images. Furthermore, the fusion attention module is designed to alleviate spectral distortion and improve contour details of the fused image. A series of ablation and contrast experiments are conducted on GF-1 and GF-2 datasets. The fusion results with less distorted pixels and more spatial details demonstrate that HARNN can implement the pansharpening task effectively, which outperforms the state-of-the-art algorithms.