The authors propose an efficient compression algorithm for hyperspectral images, which is based on the correlation coefficients adaptive asymmetric tree three-dimensional (3D) set partitioning in hierarchical trees (AT-3DSPIHT) coding of the asymmetric 3D wavelet transform (A3D-DWT) coefficients. According to the characteristics of the correlation coefficients between adjacent 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, an appropriate A3D-DWT with the corresponding decomposition levels and a proper AT-3D zerotree are determined adaptively. Several airborne visible/infrared imaging spectrometer images are used to evaluate the proposed algorithm. Compared with the state-of-the-art 3D-DWT based algorithms, the proposed adaptive AT-3DSPIHT achieves the best compression performance at lower bit rates. Moreover, at the low correlated adjacent bands, the proposed algorithm also outperforms the 2DSPIHT algorithm.