In view of the flaw that the visual connectivity of such local areas as facial features is characterized with poor quality after face completion in existing image processing methods, an edge completion method, including global discriminator network, local discriminator network and face part discriminator network, has thus been proposed, among which the global discriminator network identifies the visual connectivity of the whole graph; the local discriminator network constraints the complement part; while the face part discriminator network constraints the complements the image effect. The completed edge image can be obtained by inputting the incomplete gray image, incomplete edge image and mask image into the edge completion network, to be followed by the input of the completed edge map and incomplete color map into the image completion network, thus obtaining the completed image, with edge completion network and image completion network connected end-to-end to form a complete solution. Visual connectivity was compared with the control group on CelebA dataset, the results show that the proposed algorithm is more effective in the restoration of the information of face parts.