Limited-angle computed tomography (CT) has arisen in some medical and industrial applications. It is also a challenging problem since some scan views are missing and the directly reconstructed images often suffer from severe distortions. For such kind of problems, we analyze the features of limited-angle CT images and propose a multi-scale dilated convolution neural network (MSD-CNN) to correct the artifacts and to restore the image. In this network, the dilated convolution layer and multi-scale pooling layer are combined to form a group and exited in the whole encoder-decoder process. Since the dilated convolutions support an exponential expansion of the receptive field without losing resolution and coverage, the obtained artifact features possess the multi-scale characteristic. Furthermore, to improve the effectiveness and accuracy of the training step, we employ a preprocessing method, which extracts image patches. Numerical experiments verify the out-performance of the proposed method compared with some conventional methods, such as Unet based deep learning,TV- and L₀-based optimization methods.