How to reconstruct a high-resolution image from a single low-resolution image with plenty of details and rational hierarchy is the important problem for single image super-resolution. In this paper, we propose a novel deep neural network for single image super-resolution, called self-attention deep neural network (SADNN), where the self-attention mechanism is utilized to obtain the relationships between widely separated spatial regions. Thus, the global dependences from the features of an image are captured to promote the hierarchy of the image. Moreover, a new defined loss function, including a pixel-wise loss and a perceptual loss, is proposed to improve the image-detail reconstruction ability of the deep neural network during the training. Extensive experimental results demonstrate that the proposed method can improve texture details and the visual impression of the reconstructed high-resolution image significantly.