Utilizing orthogonal matching pursuit algorithm for compressed sensing reconstruction of hyperspectral images is to find the optimal atoms to linearly represent the original signal, so that the residual is continuously reduced to obtain the reconstructed signal. When dealing with the redundant dictionary-based reconstruction, the time consuming mainly exists in its atom matching process and residual updating process, resulting in high computational complexity and difficulty of real-time processing. Aiming at this defect, a Hermitian compressed sensing reconstruction algorithm for hyperspectral images is proposed. The main idea is Hermitian inversion lemma is used to optimize the iterative process of the residual update to improve the execution efficiency of the algorithm. In addition, the artificial fish swarm algorithm is used to find the optimal atoms and accelerate the matching process to further improve the reconstruction efficiency. The experimental results carried out on hyperspectral images show that the computational efficiency of the proposed algorithm can be improved by about 10 times compared with the traditional orthogonal matching pursuit algorithm under the condition of ensuring the reconstruction accuracy.