Band selection, by choosing a set of representative bands in hyperspectral images (HSI), is concerned to be an effective method to eliminate the 'Hughes phenomenon'. In this paper, we present a global optimal clustering-based band selection (GOC) algorithm based on the hypothesis that all the bands in a cluster are continuous at their wavelengths. After the clustering result is obtained, we propose a greedy-based method to select representative bands in each cluster, trying to minimize the linear reconstruction error. Experiment on a real HSI dataset shows that the proposed method outperforms the state-of-the-art competitors. © 2017 IEEE.