This paper proposes a new multispectral image data compression algorithm that can efficiently reduce spatial and spectral redundancies by applying classified prediction, a Karhunen-Loeve transform (KLT), and the three-dimensional set partitioning in hierarchical trees (3-D SPIHT) algorithm in the wavelet transform (WT) domain. The classification is performed in the WT domain to exploit the interband classified dependency, while the resulting class information is used for the interband prediction. The residual image data on the prediction errors between the original image data and the predicted image data is decorrelated by a KLT. Finally, the 3-D SPIHT algorithm is used to encode the transformed coefficients listed in a descending order spatially and spectrally as a result of the WT and KLT. Simulation results showed that the reconstructed images after using the proposed algorithm exhibited a better quality and higher compression ratio than those using conventional algorithms.