Aiming at the problem of high time-space complexity and inadequate usage of spectral characteristics of existing multispectral image compression algorithms, an inter-spectrum sparse equivalent representation of multispectral image and its clustering realization ways were studied. Meanwhile, a new multispectral image compression algorithm based on spectral adaptive clustering and wavelet transform was designed. The affinity propagation clustering was utilized to generate inter-spectrum sparse equivalent representation which can remove inter-spectrum redundancy under low complexity, two-dimensional wavelet transform was used to remove spatial redundancy, and set partitioning in hierarchical trees (SPIHT) was used to encode. The quality of reconstruction images was improved by error compensation mechanism. Experimental results show that the proposed approach achieves good performance in time-space complexity, the peak signal-to-noise ratio(PSNR) is significantly higher than that of similar compression algorithms under the same compression ratio, and it is a generic and effective algorithm.