Nowadays, X-ray computed tomography (CT) has been widely used in the early detection and accurate diagnosis of various diseases. However, the inherent side effect of CT radiation, relating to cancer and other diseases, has caused great concerns in radiology. So how to reduce radiation dose immensely while maintaining image quality is a major challenge in CT imaging field. As a practical application of compressed sensing theory, the sparse constraint term referred to total variation (TV) minimization has already produced promising images for low dose CT reconstruction. However, the piecewise constant assumption of TV model often produces blocky artifacts in reconstructed images. To eliminate this drawback, we apply a family of hyperbolic tangent functions to enhance the sparse representation of TV model. Furthermore, a dynamic regularization term is also introduced to improve the performance of the proposed model. In our method, the proposed constraint term is incorporated into an objective function in a statistical iterative reconstruction (SIR) framework. We evaluate the proposed method using X-ray projections collected from simulated phantoms and scanned mice. And the results show that the presented approach can produce better images when compared to several existing methods in terms of lower noise and more anatomical features.