In the field of single-image super-resolution (SISR) research, neural networks and deep learning methods are gradually being widely used by researchers. Over time, the fields of application have expanded in scope. The SISR method is also applied in the field of intelligent satellite imagery. In recent years, research applications based on intelligent satellite images have mostly focused on imaging, classification, and segmentation. They have rarely been used in actual observation problems. This article proposes a new intelligent neural network model, the Laplacian pyramid residual dense network, for the super-resolution of hyperspectral satellite medical geographic small-targets. This study proceeds in three steps. First, the three-layer Laplacian pyramid structure is designed to increase the depth of the image at the feature extraction stage. Second, the residual mode is improved and updated; a new residual block is proposed for constructing the residual dense network to enhance the feature details of the image during the training process. In the third step, an end-to-end network is established directly through the residual structure for eliminating unnecessary visualization during the process and for ease of training. According to the experimental results, it has been proved that the deep intelligent neural network method proposed here has achieved good results in the application for super-resolution of medical geographic small-target intelligent satellite images.