Abstract: Without unrolling the prior terms, most unrolling approaches for Computed Tomography (CT) reconstruction primarily unroll the fidelity term of iterative reconstruction methods to neural networks, which may reduce the computational efficiency of the reconstruction network. To overcome this drawback, a new CT reconstruction network is formed by unrolling a CT iterative reconstruction algorithm based on total variation, especially for the unfoldment of the total variation prior. The unfoldment of the prior improves the visual quality of CT reconstructed images. Firstly, the primal-dual algorithm is utilized to solve the CT reconstruction problem based on the total variation prior, to obtain an iterative reconstruction algorithm which can be easily unrolled to the neural network. Then, the unrolling approach for CT reconstruction is obtained by unrolling this iterative reconstruction algorithm. The effectiveness of the proposed algorithm is tested on a simulated low dose CT dataset. The experimental results show that, compared with six kinds of low-dose CT reconstruction algorithms, the new algorithm effectively preserves the structure and texture details of the image while removing noise in low-dose CT images. The quantitative analysis shows that the proposed algorithm scored the highest PSNR and the lowest NMSE, which indicates that the proposed algorithm is good at noise suppression in the low-dose CT reconstruction.