We present a three-dimensional (3-D) hyperspectral image compression algorithm based on zero-block coding and wavelet transforms. An efficient asymmetric 3-D wavelet transform (AT) based on the lifting technique and packet transform is used to reduce redundancies in both the spectral and spatial dimensions. The implementation via 3-D integer lifting scheme enables us to map integer-to-integer values, enabling lossy and lossless decompression from the same bit stream. To encode these coefficients after the AT, a modified 3DSPECK algorithm—asymmetric transform 3-D set-partitioning embedded block (AT-3DSPECK) is proposed. According to the distribution of energy of the transformed coefficients, the 3DSPECK's 3-D set partitioning block algorithm and the 3-D octave band partitioning scheme are efficiently combined in the proposed AT-3DSPECK algorithm. Several AVIRIS (Airborne Visible/Infrared Imaging Spectrometer) images are used to evaluate the compression performance. Compared with the JPEG2000, AT-3DSPIHT, and 3DSPECK lossless compression techniques, the AT-3DSPECK achieves the best lossless performance. In lossy mode, the AT-3DSPECK algorithm outperforms AT-3DSPIHT and 3DSPECK at all rates. Besides the high compression performance, AT-3DSPECK supports progressive transmission. Clearly, the proposed AT-3DSPECK algorithm is a better candidate than several conventional methods.