Band selection is an important preprocessing step for hyperspectral image processing. Many valid criteria have been proposed for band selection, and these criteria model band selection as a single-objective optimization problem. In this paper, a novel multiobjective model is first built for band selection. In this model, two objective functions with a conflicting relationship are designed. One objective function is set as information entropy to represent the information contained in the selected band subsets, and the other one is set as the number of selected bands. Then, based on this model, a new unsupervised band selection method called multiobjective optimization band selection (MOBS) is proposed. In the MOBS method, these two objective functions are optimized simultaneously by a multiobjective evolutionary algorithm to find the best tradeoff solutions. The proposed method shows two unique characters. It can obtain a series of band subsets with different numbers of bands in a single run to offer more options for decision makers. Moreover, these band subsets with different numbers of bands can communicate with each other and have a coevolutionary relationship, which means that they can be optimized in a cooperative way. Since it is unsupervised, the proposed algorithm is compared with some related and recent unsupervised methods for hyperspectral image band selection to evaluate the quality of the obtained band subsets. Experimental results show that the proposed method can generate a set of band subsets with different numbers of bands in a single run and that these band subsets have a stable good performance on classification for different data sets.