Band selection is a crucial preprocessing step for hyperspectral image classification, which is a classic feature selection method. Feature selection is designed to select feature subsets to represent the whole feature space. For feature selection, two crucial issues need to be handled: preserving information and redundancy reducing. In this paper, a novel feature selection method for hyperspectral image classification is proposed, which is based on a newly designed memetic algorithm. In the proposed method, a suitable objective function is designed, which can measure the contained crucial information and redundancy information in the selected feature subsets. To optimize this objective function efficiently, a novel memetic algorithm is designed. The genetic operator and local search strategy are newly designed according to the characteristic of hyperspectral images. Experiments are implemented on three real data sets compared with some state of arts. The experimental results show that the proposed method can obtain stable and superior feature subsets for classification.