Deep iterative unfolding networks have garnered a lot of attention lately because of their great learning capabilities and good interpretability. The regularization terms in existing CT image reconstruction methods mostly focus on information within a specific domain, leading to issues such as edge blurring and information loss in the reconstructed results. Therefore, a sparse transform prior constrain based deep unfolding network is proposed for sparse-view CT reconstruction. Two regularization terms with complementary information—transform-domain sparse regularization and pixel-domain consistency regularization—are created in consideration of the important roles that both pixel-domain and transform-domain information play in picture reconstruction. Based on these, the objective function for sparse-view CT reconstruction is redesigned. Furthermore, a new deep unfolding network for iterative reconstruction of low-dose CT is created by mapping a set of constraint relationships established from an iterative optimization solution for the constructed objective function. Experimental results demonstrate that the algorithm presented in this paper achieves a great improvement on average peak signal to noise ratio (PSNR) and visual information fidelity (VIF) compared to the classical FISTA algorithms.