Abstract: In order to improve the quality of image reconstruction, a non-local image reconstruction algorithm based on low rank constraint is proposed based on compressed sensing theory. Shepp-Logan head phantom and real brain CT slices were used for reconstruction, and the peak signal-to-noise ratio (PSNR) was used as the evaluation standard of reconstructed image quality, and the reconstruction results of other two reconstruction algorithms were compared. After a certain number of iterations, the reconstructed image results based on this algorithm were closer to the original image, and the convergence time was earlier. The experimental results show that the proposed algorithm is superior to the contrast algorithm in terms of reconstruction quality and convergence speed.