In this paper, a novel hyperspectral denoising method is proposed, aiming at restoring clean images from images disturbed by complex noise. Previous denoising methods have mostly focused on exploring the spatial and spectral correlations of hyperspectral data. The performances of these methods are often limited by the effective information of the neighboring bands of the image patches in the spectral dimension, as the neighboring bands often suffer from similar noise interference. On the contrary, this study designed a cross-band non-local attention module with the aim of finding the optimal similar band for the input band. To avoid being limited to neighboring bands, this study also set up a memory library that can remember the detailed information of each input band during denoising training, fully learning the spectral information of the data. In addition, we use dense connected module to extract multi-scale spatial information from images separately. The proposed network is validated on both synthetic and real data. Compared with other recent hyperspectral denoising methods, the proposed method not only demonstrates good performance but also achieves better generalization.