With recent increases in the number of network-connected devices, the number of edge computing services that provide similar functions has increased. Therefore, it is important to recommend an optimal edge computing service, based on quality-of-service (QoS). However, in the real world, there is a cold-start problem in QoS data: highly sparse invocation. Therefore, it is difficult to recommend a suitable service to the user. Deep learning techniques were applied to address this problem, or context information was used to extract deep features between users and services. However, edge computing environment has not been considered in previous studies. Our goal is to predict the QoS values in real edge computing environments with improved accuracy. To this end, we propose a GAIN-QoS technique. It clusters services based on their location information, calculates the distance between services and users in each cluster, and brings the QoS values of users within a certain distance. We apply a Generative Adversarial Imputation Nets (GAIN) model and perform QoS prediction based on this reconstructed user service invocation matrix. When the density is low, GAIN-QoS shows superior performance to other techniques. In addition, the distance between the service and user slightly affects performance. Thus, compared to other methods, the proposed method can significantly improve the accuracy of QoS prediction for edge computing, which suffers from cold-start problem.