Single image super-resolution is an ill-posed problem, which aims to reconstruct the texture pattern with the given blurry and low-resolution image. Recently, Convolution Neural Network (CNN) was introduced into the field of super-resolution. Although excellent performance was obtained by current studies through designing the structure and the connection way of CNN, the use of edge data for training more powerful model was ignored. Therefore, a method based on edge data enhancement, that is, Non-local Channel Attention (NCA) method for single image super-resolution was proposed. The proposed method can make full use of the training data and improve performance by non-local channel attention. Not only the guideline to design the network was provided by the proposed method, but also the interpretation of super-resolution task was able to be performed by using the proposed method. The NCA Network (NCAN) model was composed of main branch and edge enhancement branch. The main branch self-attention was made for reconstructing the super-resolution images by taking the low-resolution images as input of the model and predicting the edge data. Experimental results show that, compared with the Second-order Attention Network (SAN) model, NCAN has the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity (SSIM) improved by 0.21 dB and 0.009 respectively on the benchmark dataset BSD100 at the magnification factor of 3; compared with the deep Residual Channel Attention Network (RCAN) model, NCAN has the PSNR and SSIM significantly improved on benchmark datasets of Set5 and Set14 at the magnification factor of 3 and 4. NCAN outperforms the state-of-the-art models on comparable parameters.