Hyperspectral images are massive data consisting of hundreds of spectral bands and have been used in a large number of applications. With growth of spectral resolution and spatial resolution of hyperspectral data， data size increases rapidly. How to effectively compress hyperspectral image becomes a key problem that affects the development and popularization of hyperspectral image. Recently， DWT-based methods have been proved promising for hyperspectral image. But their performances are restricted because it is difficult for them to efficiently take advantage of the various properties of hyperspectral image. For the traditional wavelet transform, the specific properties of hyperspectral images are basically utilized by corresponding to characteristics of wavelet coefficients. So the present paper proposes a new DWT-based method using decorrelation technique according to the spectral characters of hyperspectral image. Block predictive coding is designed to remove the spectral correlation as well as spatial correlation simultaneously and is applied into the DWT-based method. Firstly, hyperspectral image is divided into several image blocks. The bands in a single block possess high spectral correlation. Afterwards, it is deduced that bands of a single block tend to be proportional in altitudes. Bands prediction, which is done in the range of each block respectively, is designed according to this and others characteristics of hyperspectral images. Finally, reference bands of block prediction and the deviation data obtained after block prediction are compressed by 2D-DWT algorithm and 3D-DWT algorithm respectively. Experiment results indicate that compared with the well known techniques the proposed method can significantly improve SNR and PSNR performance, even to 4.2 dB (compared with AT-3DSPIHT algorithm). And the code efficiency at low bit rates is also competitive.