Synchrotron radiation can be used as a light source in X-ray microscopy to acquire a high-resolution image of a microscale object for tomography. However, numerous projections must be captured for a high-quality tomographic image to be reconstructed; thus, image acquisition is time consuming. Such dense imaging is not only expensive and time consuming but also results in the target receiving a large dose of radiation. To resolve these problems, sparse acquisition techniques have been proposed; however, the generated images often have many artefacts and are noisy. In this study, a deep-learning-based approach is proposed for the tomographic reconstruction of sparse-view projections that are acquired with a synchrotron light source; this approach proceeds as follows. A convolutional neural network (CNN) is used to first interpolate sparse X-ray projections and then synthesize a sufficiently large set of images to produce a sinogram. After the sinogram is constructed, a second CNN is used for error correction. In experiments, this method successfully produced high-quality tomography images from sparse-view projections for two data sets comprising Drosophila and mouse tomography images. However, the initial results for the smaller mouse data set were poor; therefore, transfer learning was used to apply the Drosophila model to the mouse data set, greatly improving the quality of the reconstructed sinogram. The method could be used to achieve high-quality tomography while reducing the radiation dose to imaging subjects and the imaging time and cost.