With the increasing spectral dimension of hyperspectral images (HSI), how correctly choose bands based on band correlation and information has become more significant, but also complicated. Band selection is a combinatorial optimization problem, and intelligent optimization algorithms have been shown to be crucial in solving combinatorial optimization problems. However, major of them only use a single objective as the selection index, while neglecting the overall features of hyperspectral images, which may lead to inaccuracy in object detection. To tackle this, we propose a band selection method based on a multi-objective cuckoo search algorithm (MOCS) when constructing a multi-objective unsupervised band selection model based on the amount of information and correlation of the bands (MOCS-BS). Specifically, an adaptive strategy based on population crowding degree is first proposed to assist Lévy flight in overcoming the influence of the parameter constancy. Then, an information-sharing strategy based on grouping and crossover is designed to balance the search ability between global exploration and local exploitation, which can overcome the shortcomings caused by the lack of information interaction between individuals. Finally, the HSI classification experiments are performed by Random Forest and KNN classifiers based on the subset of bands selected by the proposed MOCS-BS method. The proposed method is compared with state-of-the-art algorithms including neighborhood grouping normalized matched filter (NGNMF) and multi-objective artificial bee colony with band selection (MABC-BS) on four HSI datasets. The experimental results demonstrate that MOCS-BS is more effective and robust than other methods.