Nowadays online users prefer to join multiple social media for the purpose of socialized online service. The problem \textit{anchor link prediction} is formalized to link user data with the common ground on user profile, content and network structure across social networks. Most of the traditional works concentrated on learning matching function with explicit or implicit features on observed user data. However, the low quality of observed user data confuses the judgment on anchor links, resulting in the matching collision problem in practice. In this paper, we explore local structure consistency and then construct a matching graph in order to circumvent matching collisions. Furthermore, we propose graph convolution networks with mini-batch strategy, efficiently solving anchor link prediction on matching graph. The experimental results on three real application scenarios show the great potentials of our proposed method in both prediction accuracy and efficiency. In addition, the visualization of learned embeddings provides us a qualitative way to understand the inference of anchor links on the matching graph.