Matrix completion with rating data and auxiliary information for users and items is a challenging task in recommendation systems. In this paper, we propose an end-to-end architecture named Attention-based Graph Convolutional Network (AGCN) to embed both rating data and auxiliary information in a unified space, and subsequently learn low-rank dense representations via graph convolutional networks and attention layers. Compared to previous work, AGCN reduces computational complexity with Chebyshev polynomial graph filters. The introduced attention layer, which encourages weighing the neighbor information to learn more expressive structural graph representations, can improve the prediction accuracy, and lead to faster and more stable convergence. Experimental results show that our model can perform better and converge faster than current state-of-the-art methods on the real-world MovieLens and Flixster datasets.