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In this paper, we propose an algorithm for reference bands selection in hyperspectral image (HSI) compression. In HSI compression, many algorithms need to select the reference bands, but all those algorithms uniformly select the reference bands. The uniform selection method isn't optimal, so we propose a genetic algorithm (GA) based reference band selection method to get lower prediction residual. The proposed method has the advantage of being simple, yielding compression fidelity better than the classical methods.