With the development of deep learning, considerable progress has been made in image restoration. Notably, many state-of-the-art single image super-resolution (SR) methods have been proposed. However, most of them contain many parameters, which leads to a significant amount of calculation consumption in the inference phase. To make current SR networks more lightweight and resource-friendly, we present a convolution neural network with the proposed selective channel processing strategy (SCPN). Specifically, the selective channel processing module (SCPM) is first designed to dynamically learn the significance of each channel in the feature map using a channel selection matrix in the training phase. Correspondingly, in the inference phase, only the essential channels indicated by the channel selection matrixes need to be further processed. By doing so, we can significantly reduce the parameters and the calculation consumption. Moreover, the differential channel attention (DCA) block is proposed, which takes into consideration the data distribution of the channels in feature maps to restore more high-frequency information. Extensive experiments are performed on the natural image super-resolution benchmarks (i.e., Set5, Set14, B100, Urban100, Manga109) and remote-sensing benchmarks (i.e., UCTest and RESISCTest), and our method achieves superior results to other state-of-the-art methods. Furthermore, our method keeps a slim size with fewer than 1 M parameters, which proves the superiority of our method. Owing to the proposed SCPM and DCA, our SCPN model achieves a better trade-off between calculation cost and performance in both general and remote-sensing SR applications, and our proposed method can be extended to other computer vision tasks for further research.