Computed tomography (CT) is one of the most important medical imaging technologies in use today. Most commercial CT products use a technique known as the filtered backprojection (FBP) that is fast and can produce decent image quality when an X-ray dose is high. However, the FBP is not good enough on low-dose X-ray CT imaging because the CT image reconstruction problem becomes more stochastic. A more effective reconstruction technique proposed recently and implemented in a limited number of CT commercial products is an iterative reconstruction (IR). The IR technique is based on a Bayesian formulation of the CT image reconstruction problem with an explicit model of the CT scanning, including its stochastic nature, and a prior model that incorporates our knowledge about what a good CT image should look like. However, constructing such prior knowledge is more complicated than it seems. In this article, we propose a novel neural network for CT image reconstruction. The network is based on the IR formulation and constructed with a recurrent neural network (RNN). Specifically, we transform the gated recurrent unit (GRU) into a neural network performing CT image reconstruction. We call it "GRU reconstruction." This neural network conducts concurrent dual-domain learning. Many deep learning (DL)-based methods in medical imaging are single-domain learning, but dual-domain learning performs better because it learns from both the sinogram and the image domain. In addition, we propose backpropagation through stage (BPTS) as a new RNN backpropagation algorithm. It is similar to the backpropagation through time (BPTT) of an RNN; however, it is tailored for iterative optimization. Results from extensive experiments indicate that our proposed method outperforms conventional model-based methods, single-domain DL methods, and state-of-the-art DL techniques in terms of the root mean squared error (RMSE), the peak signal-to-noise ratio (PSNR), and the structure similarity (SSIM) and in terms of visual appearance.