Aiming at the problems of insufficient detail and over smooth in current face super-resolution algorithms, an algorithm for the Single Image Super-Resolution Reconstruction based on the Generative Adversarial Network(GAN) is proposed. The algorithm connects the edge detection network in parallel in the generation network, extracting abundant face contour details to assist in feature extraction, optimizing the network training process through the Ranger optimizer. Finally, establish a mathematical model to comprehensively evaluate the reconstruction effect combining objective assessment and subjective assessment indicators. The experimental results show that the algorithm has better subjective and objective effects than the Cubic Spline Method, SRGAN, FSRCNN, etc. It is proved that the algorithm improves the reconstruction ability of facial details and has a better reconstruction effect.