In the medical field, computed tomography (CT) is a commonly used examination method, but the radiation generated increases the risk of illness in patients. Therefore, low-dose scanning schemes have attracted attention, in which noise reduction is essential. We propose a purposeful and interpretable decomposition iterative network (DISN) for low-dose CT denoising. This method aims to make the network design interpretable and improve the fidelity of details, rather than blindly designing or using deep CNN architecture. The experiment is trained and tested on multiple data sets. The results show that the DISN method can restore the low-dose CT image structure and improve the diagnostic performance when the image details are limited. Compared with other algorithms, DISN has better quantitative and visual performance, and has potential clinical application prospects.