In recent years, with the rapid development of deep learning, super-resolution methods based on convolutional neural networks (CNNs) have made great progress. However, the parameters and the required consumption of computing resources of these methods are also increasing to the point that such methods are difficult to implement on devices with low computing power. To address this issue, we propose a lightweight single image super-resolution network with an expectation-maximization attention mechanism (EMASRN) for better balancing performance and applicability. Specifically, a progressive multi-scale feature extraction block (PMSFE) is proposed to extract feature maps of different sizes. Furthermore, we propose an HR-size expectation-maximization attention block (HREMAB) that directly captures the long-range dependencies of HR-size feature maps. We also utilize a feedback network to feed the high-level features of each generation into the next generation's shallow network. Compared with the existing lightweight single image super-resolution (SISR) methods, our EMASRN reduces the number of parameters by almost one-third. The experimental results demonstrate the superiority of our EMASRN over state-of-the-art lightweight SISR methods in terms of both quantitative metrics and visual quality. The source code can be downloaded at https://github.com/xyzhu1/EMASRN .