A neural network that outputs reconstructed images based on projection data containing scattered X-rays is presented, and the proposed scheme exhibits better accuracy than conventional computed tomography (CT), in which the scatter information is removed. In medical X-ray CT, it is a common practice to remove scattered X-rays using a collimator placed in front of the detector. In this study, the scattered X-rays were assumed to have useful information, and a method was devised to utilize this information effectively using a neural network. Therefore, we generated 70,000 projection data by Monte Carlo simulations using a cube comprising 216 (6 × 6 × 6) smaller cubes having random density parameters as the target object. For each projection simulation, the densities of the smaller cubes were reset to different values, and detectors were deployed around the target object to capture the scattered X-rays from all directions. Then, a neural network was trained using these projection data to output the densities of the smaller cubes. We confirmed through numerical evaluations that the neural-network approach that utilized scattered X-rays reconstructed images with higher accuracy than did the conventional method, in which the scattered X-rays were removed. The results of this study suggest that utilizing the scattered X-ray information can help significantly reduce patient dosing during imaging.