This article proposes a multiscale spectral features graph fusion (MSFGF) method for selecting proper hyperspectral bands. The MSFGF regards that the selected bands should reflect diagnostic spectral information of ground objects at different scales, and it explores band selection from the aspect of multiple spatial scales. First, it adopts the multiscale low-rank decomposition (MSLRD) model to find multiscale spectral features of different ground objects. The model considers divergent spatial structures or spatial correlations of ground objects at different scales, and factorizes the hyperspectral data cube into a series of low-rank block-wise data cubes, where the blocks take spatial structures of different ground objects at increasing scales. Second, the MSFGF presents the multiscale sparse spectral clustering (MSSC) model to fuse the separate connected graphs of multiscale spectral features into a consensus graph. The consensus graph combines the complementary information of multiscale spectral features and helps to reveal the intrinsic clustering structure of all spectral bands. Finally, the MSFGF utilizes spectral clustering to find clusters from the consensus graph and selects representative bands. Experimental results on three widely used hyperspectral data prove the superiority of MSFGF in selecting bands, where it outperforms other seven state-of-the-art methods in classification with an acceptable computational cost.