Hyperspectral images (HSI) present a wealth of information. It is distinguished by its high dimensionality. It served humanity in many fields. The quantity of HSI information represents a double-edged sword. As a consequence, their dimensionality must be reduced. Nowadays, several methods are proposed to overcome their duress. The most useful and essential solution is selection approaches of hyperspectral bands to analyze it quickly. Our work suggests a novel method to achieve this selection: we introduce a Genetic Algorithm (GA) based on mutual information (MI) and Normalized Mutual Information (NMI) as fitness functions. It selects the relevant bands from noisiest and redundant ones that don’t contain any additional information. .The proposed method is applied to three different HSI: INDIAN PINE, PAVIA, and SALINAS. The introduced algorithm provides a remarkable efficiency on the accuracy of the classification, in front of other statistical methods: the Bhattacharyya coefficient as well as the inter-bands correlation (Pearson correlation). We conclude that the measure of information (MI, NMI) provides more efficiency as a fitness function for GA selection applied to HSI; it must be more investigated.