Hyperspectral band selection plays an important role in overcoming the curse of dimensionality. Recently, clustering-based band selection methods have shown promise in the selection of informative and representative bands from hyperspectral images (HSIs). However, most existing clustering-based band selection methods involve the clustering of original HSIs, limiting their performance because of the high dimensionality of hyperspectral bands. To tackle this problem, a novel hyperspectral band selection method termed joint learning of correlation-constrained fuzzy clustering and discriminative non-negative representation for hyperspectral band selection (CFNR) is presented. In CFNR, graph regularized non-negative matrix factorization (GNMF) and constrained fuzzy C-means (FCM) are integrated into a unified model to perform clustering on the learned feature representation of bands rather than on the original high-dimensional data. Specifically, the proposed CFNR aims to learn the discriminative non-negative representation of each band for clustering by introducing GNMF into the model of the constrained FCM and making full use of the intrinsic manifold structure of HSIs. Moreover, based on the band correlation property of HSIs, a correlation constraint, which enforces the similarity of clustering results between neighboring bands, is imposed on the membership matrix of FCM in the CFNR model to obtain clustering results that meet the needs of band selection. The alternating direction multiplier method is adopted to solve the joint optimization model. Compared with existing methods, CFNR can obtain a more informative and representative band subset, thus can improve the reliability of hyperspectral image classifications. Experimental results on five real hyperspectral datasets demonstrate that CFNR can achieve superior performance compared with several state-of-the-art methods.