Considering the strong correlation between adjacent band images of hyperspectral data in combination with the fast searching ability of the particle swarm optimization algorithm, a sparse decomposition algorithm of hyperspectral images based on spectral correlation is proposed. The hyperspectral images are divided into reference and common band images. Particle swarm optimization is performed on the reference band images to find the optimal atoms and realize their sparse decomposition. The optimal atoms of a common band image consist of two parts. Parts of these atoms are inherited from the optimal atoms of the reference band images, and the number of inheritances is determined by the spectral correlation between the common and reference band images. The remaining atoms are obtained using particle swarm optimization. The experimental results on hyperspectral data show that in cases with the same reconstruction accuracy, the sparse decomposition rate is approximately 18 times higher than the orthogonal matching pursuit algorithm.