Remote sensing image super-resolution (SR) plays an essential role in many remote sensing applications. Recently, remote sensing image super-resolution methods based on deep learning have shown remarkable performance. However, directly utilizing the deep learning methods becomes helpless to recover the remote sensing images with a large number of complex objectives or scene. So we propose an edge-based dense connection generative adversarial network (SREDGAN), which minimizes the edge differences between the generated image and its corresponding ground truth. Experimental results on NWPU-VHR-10 and UCAS-AOD datasets demonstrate that our method improves 1.92 and 0.045 in PSNR and SSIM compared with SRGAN, respectively.