Single image super-resolution is an effective way to enhance the spatial resolution of remote sensing image, which is crucial for many applications such as target detection and image classification. However, existing methods based on the neural network usually have small receptive fields and ignore the image detail. We propose a novel method named deep memory connected network (DMCN) based on a convolutional neural network to reconstruct high-quality super-resolution images. We build local and global memory connections to combine image detail with environmental information. To further reduce parameters and ease time-consuming, we propose downsampling units, shrinking the spatial size of feature maps. We test DMCN on three remote sensing datasets with different spatial resolution. Experimental results indicate that our method yields promising improvements in both accuracy and visual performance over the current state-of-the-art.