High-resolution ocean remote sensing images are of vital importance in the research field of ocean remote sensing. However, the available ocean remote sensing images are composed of averaged data, whose resolution is lower than the instant remote sensing images. In this paper, we propose a very deep super-resolution learning model for remote-sensing image super-resolution. In our research, we target satellite-derived sea surface temperature (SST) images, a typical kind of ocean remote sensing image, as a specific case study of super-resolution on remote sensing images. In this paper, we propose a novel model architecture based on the very deep super-resolution (VDSR) model, to further enhance its performance. Furthermore, we evaluate the peak signal-to-noise ratio (PSNR) and perceptual loss of the model trained on the natural images and SST frames. We designed and applied our model to the China Ocean SST database, the Ocean SST database, and the Ocean-Front databases, all containing remote sensing images captured by advanced very high resolution radiometers (AVHRR). Experimental results show that our model performs better than the state-of-the-art models on SST frames.