In this paper, we propose an efficient compression algorithm for hyperspectral images. It is based on the correlation coefficients adaptive AT-3DSPIHT coding in the domain of WPT (wavelet packet transform). According to the characteristics of correlation coefficients between spectral bands, a binary tree spectral band grouping algorithm is carried out to divide the adjacent spectral bands into different mode groups. Along with this, WPT with the corresponding decomposition levels and a proper AT-3D zerotree are determined adaptively. Several AVIRIS images are used to evaluate the proposed algorithm. Compared with the existing 3D-based algorithms, the proposed adaptive AT-3DSPIHT achieves the best compression performance at lower rates. Moreover, at the low correlated adjacent bands, our proposed algorithm also beats the 2DSPIHT and JPEG2000-MC algorithm respectively.