Recently, deep convolutional neural networks (CNNs) have been widely explored in single image super-resolution (SISR) and obtained remarkable performance. However, most of the existing CNN-based SISR methods mainly focus on wider or deeper architecture design, neglecting to explore the feature correlations of intermediate layers, hence hindering the representational power of CNNs. To address this issue, in this paper, we propose a second-order attention network (SAN) for more powerful feature expression and feature correlation learning. Specifically, a novel train- able second-order channel attention (SOCA) module is developed to adaptively rescale the channel-wise features by using second-order feature statistics for more discriminative representations. Furthermore, we present a non-locally enhanced residual group (NLRG) structure, which not only incorporates non-local operations to capture long-distance spatial contextual information, but also contains repeated local-source residual attention groups (LSRAG) to learn increasingly abstract feature representations. Experimental results demonstrate the superiority of our SAN network over state-of-the-art SISR methods in terms of both quantitative metrics and visual quality.