This paper proposes a retransmission control system based on image recognition accuracy as a traffic reduction technique for improving network bandwidth usage efficiency in image recognition service using wireless edge computing. For traffic reduction, image compression is useful. However, it is known to deteriorate the recognition accuracy. Our proposed system is applied to guarantee this deterioration. By retransmitting images according to the recognition accuracy, we aim to reduce traffic and to guarantee recognition accuracy. When compressing the image, PSNR is calculated to adaptively change the ratio of the image compression, to maintain the image quality. This paper uses down-sampler as an image compression method and demonstrates the effectiveness of the proposed system through a wireless network simulation. We confirm that our proposed retransmission system can reduce the network traffic congestion, and guarantee the recognition accuracy as same as the conventional method.