Hyperspectral imaging sensors can acquire images in hundreds of continuous narrow spectral bands. Therefore each object presented in the image can be identified from their spectral response. However, such kind of imaging brings a huge amount of data, which requires transmission, processing, and storage resources for both airborne and space borne imaging. Due to the high volume of hyperspectral image data, the exploration of compression strategies has received a lot of attention in recent years. Compression of hyperspectral data cubes is an effective solution for these problems. Lossless compression of the hyperspectral data usually results in low compression ratio, which may not meet the available resources; on the other hand, lossy compression may give the desired ratio, but with a significant degradation effect on object identification performance of the hyperspectral data. Moreover, most hyperspectral data compression techniques exploits the similarities in spectral dimensions; which requires bands reordering or regrouping, to make use of the spectral redundancy. In this paper, we explored the spectral cross correlation between different bands, and proposed an adaptive band selection method to obtain the spectral bands which contain most of the information of the acquired hyperspectral data cube. The proposed method mainly consist three steps: First, the algorithm decomposes the original hyperspectral imagery into a series of subspaces based on the hyper correlation matrix of the hyperspectral images between different bands. And then the Wavelet-based algorithm is applied to the each subspaces. At last the PCA method is applied to the wavelet coefficients to produce the chosen number of components. The performance of the proposed method was tested by using ISODATA classification method.