Abstract: How to reduce the storage and transmission cost of mass hyperspectral data is concerned with growing interest. This paper proposes a hyperspectral data compression algorithm using sparse representation. First, a training sample set is constructed with a band selection algorithm, and then all hyperspectral bands are coded sparsely using a basis function dictionary learned from the training set. Finally, the position indices and values of the non-zero elements are entropy coded to finish the compression. Experimental results reveal that the proposal algorithm achieves better nonlinear approximation performance than 3D-DWT and outperforms 3D-SPIHT. Besides, the algorithm has better performance in spectral information preservation.