This paper presents an image reconstruction method combining convolution neural networks (CNN) with anchored neighborhood regression (ANR), aiming at the shortcomings of the conventional anchored neighborhood regression (ANR) image superresolution method, which is inflexible and incapable to restore image details. Firstly, the elastic network regression model is proposed in ANR to give the algorithm with the characteristics of feature selection. Secondly, the lanczos3 interpolation method is used in the part of image preprocessing of CNN to accelerate the operation speed. In the feature extraction, the Swish function with selfgating characteristics is proposed as the activation function to improve the test accuracy. Finally, the correlation coefficient of the image is proposed in the evaluation of the reconstructed image and used for further evaluation of the reconstructed image. The experimental results show that the average PSNR, average SSIM and average correlation coefficient of the proposed method reach 0.982 8, 0.968 and 0.938 0 respectively. The algorithm effectively restores the details of the image and the image quality is further improved.