For the sparse angle projection data, the problem of artifact and noise is easy to appear in the image reconstruction of computed tomography, which is difficult to meet the requirements of industrial and medical diagnosis. In this paper, a sparse angle CT iterative reconstruction algorithm based on overlapping group sparsity and hyper-Laplacian prior is proposed. The overlapping group sparsity reflects the sparsity of image gradient, and the overlapping cross relation between the adjacent elements is considered from the perspective of the image gradient. The hyper-Laplacian prior can accurately approximate the heavy-tailed distribution of the image gradient and improve the overall quality of the reconstructed image. The algorithm model proposed in this paper uses alternating direction multiplier method, principal component minimization method and gradient descent method to solve the objective function. The experimental results show that under the condition of the sparse angle CT reconstruction, the proposed algorithm has certain improvement in preserving structural details and suppressing noise and staircase artifacts generated in the process of image reconstruction.