Deep convolutional neural networks (CNNs) have been widely used and achieved state-of-the-art performance in many image or video processing and analysis tasks. In particular, for image super-resolution (SR) processing, previous CNN-based methods have led to significant improvements, when compared with shallow learning-based methods. However, previous CNN-based algorithms with simple direct or skip connections are of poor performance when applied to remote sensing satellite images SR. In this study, a simple but effective CNN framework, namely deep distillation recursive network (DDRN), is presented for video satellite image SR. DDRN includes a group of ultra-dense residual blocks (UDB), a multi-scale purification unit (MSPU), and a reconstruction module. In particular, through the addition of rich interactive links in and between multiple-path units in each UDB, features extracted from multiple parallel convolution layers can be shared effectively. Compared with classical dense-connection-based models, DDRN possesses the following main properties. (1) DDRN contains more linking nodes with the same convolution layers. (2) A distillation and compensation mechanism, which performs feature distillation and compensation in different stages of the network, is also constructed. In particular, the high-frequency components lost during information propagation can be compensated in MSPU. (3) The final SR image can benefit from the feature maps extracted from UDB and the compensated components obtained from MSPU. Experiments on Kaggle Open Source Dataset and Jilin-1 video satellite images illustrate that DDRN outperforms the conventional CNN-based baselines and some state-of-the-art feature extraction approaches.