This paper proposes a new multispectral image data compression algorithm (KLT/WT-3DEZB). The proposed coding strategy consists of three main steps. Firstly, a wavelet transform (WT) is applied to reduce the spatial redundancies. Then, a Karhunen-Loeve transform (KLT) is used to reduce the redundancies in the spectral domain. Finally, a modified SPECK algorithm---three-dimensional embedded zeroblock (3DEZB) algorithm is proposed and used to encode the transformed coefficients. Numerical experiments show that the reconstructed images using the proposed algorithm exhibite a better quality and a higher compression ratio than those obtained by traditional KLT/WT-3DSPIHT, 3DSPIHT, and 3DSPECK algorithms.