A novel low-dose reconstruction algorithm using dynamic optimization design was developed to suppress artifacts and noise in computed tomography (CT) imaging under the low-dose scan protocols. In this paper, a family of hyperbolic tangent functions was selected to build the composite function model of fractional total variation (TpV). Furthermore, a dynamic optimization (DO) term was also applied to improve the performance of the presented model. In our method, the proposed iterative reconstruction was achieved via the statistical iterative reconstruction (SIR) framework. Then, the presented approach was evaluated by using X-ray low dose projections collected from simulated phantom and scanned mice. The simulated results for 180 sampling views show that the signal to noise ratios (SNR) of images reconstructed by the proposed algorithm are 29.51, 8.03, 9.15, 6.81 dB higher than those of images reconstructed by filtered back-projection algorithm, TpV algorithm, and adaptively reweighted total variation algorithm, respectively. And the mouse data studies demonstrate that the proposed method suppresses artifacts or noise successfully and preserves more soft tissue details in reconstructed images. Moreover, the quality of reconstructed images can be greatly improved by the presented low-dose reconstruction algorithm.