Satellite remote sensing has wide applications in many fields. However, the quality of the observed images captured from the satellite sensors exhibits significant variances and most images are low resolution. Therefore, they adversely affect the system performance in a variety of real-world applications such as object recognition and analysis. In order to enhance the resolution of remote sensing images, we propose a super-resolution neural network called progressive residual depth neural network (PRDNN). The progressive residual structure used by PRDNN can gradually discover the feature information of satellite images at different levels and different receptive fields, thus providing more detailed features for reconstructing super-resolution satellite images. The experimental results of the DOTA satellite image database demonstrate that the proposed method is superior to the most advanced super-resolution algorithm in recent years.