Space object recognition is the basis of space attack and defense confrontation. High-quality space object images are very important for space object recognition. Because of the large number of cosmic rays in the space environment and the inadequacy of optical lenses and detectors on satellites to support high-resolution imaging, most of the images obtained are blurred and contain a lot of cosmic-ray noise. So, denoising methods and super-resolution methods are two effective ways to reconstruct high-quality space object images. However, most super-resolution methods could only reconstruct the lost details of low spatial resolution images, but could not remove noise. On the other hand, most denoising methods especially cosmic-ray denoising methods could not reconstruct high-resolution details. So in this paper, a deep convolutional neural network (CNN)-based single space object image denoising and super-resolution reconstruction method is presented. The noise is removed and the lost details of the low spatial resolution image are well reconstructed based on one very deep CNN-based network, which combines global residual learning and local residual learning. Based on a dataset of satellite images, experimental results demonstrate the feasibility of our proposed method in enhancing the spatial resolution and removing the noise of the space objects images.