Though reducing the number of projection angles or lowering the current intensity of X-ray tube can reduce radiation dose and therefore alleviate damage to human bodies, the former measure can result in incomplete projection data while the later causes a declined signal to noise ratio of projection data. We propose a low-dose CT image statistical iterative reconstruction algorithm based on sparsity constraint in shearlet domain. The statistical weighting coefficient of data fidelity terms is introduced to reduce the influence of noise on the reconstruction results, and the sparse representation of intermediate images in shearlet domain is added into the objective function as a regularization item by means of the augmented Lagrangian method so as to narrow down the solution space and obtain stable and accurate reconstruction from incomplete projection data. According to experimental data, this algorithm can get high-quality images when projection data is far from completeness or the signal to noise ratio of projection data declines sharply. The proposed algorithm can be used for attaining reconstructed images that clearly keep structural details when the radiation dose is decreased to 10% of the filtered back projection (FBP) or even lower degrees.