The compression of hyperspectral images (HSIs) has recently become a very attractive issue for remote sensing applications because of their volumetric data. In this paper, an efficient method for hyperspectral image compression is presented. The proposed algorithm, based on Discrete Wavelet Transform and Tucker Decomposition (DWT-TD), exploits both the spectral and the spatial information in the images. The core idea behind our proposed technique is to apply TD on the DWT coefficients of spectral bands of HSIs. We use DWT to effectively separate HSIs into different sub-images and TD to efficiently compact the energy of sub-images. We evaluate the effect of the proposed method on real HSIs and also compare the results with the well-known compression methods. The obtained results show a better performance of the proposed method. Moreover, we show the impact of compression HSIs on the supervised classification and linear unmixing.