Image completion is an important research content in the field of digital image processing, and the completion of large area irregular missing images is a research hotspot in recent years. However, the existing image completion technology has some limitations. The method based on generative adversarial network ignores the edge structure information of the image, and it can't restore the fine details. The method based on local discriminator can't deal with the missing irregular image, and the completion task doesn't conform to the actual application scene. Combined with the idea of multi-granularity cognitive computing, this paper proposes an edge discriminator based on multi-granularity feature fusion, which can fully learn the edge structure information of different granularity, improve the consistency between the generated image edge and the real image edge, and generate the complete image with clearer structure. At the same time, the edge space attenuation loss is introduced, which can improve the continuity of edge pixels. In addition, the attention mechanism is used to optimize the local discriminator to process the irregular missing image. Experimental results on Places2, Paris Streetview and other public datasets show that the proposed method achieves better results than other image completion methods in the completion of large areas of irregular missing images, which illustrates the importance of edge structure information in image completion research to a certain extent.