Face clustering is a necessary tool in the field of face-related algorithm research, which is widely used in album management and unlabeled data management. Recent works which use Graph Convolution Network (GCN) to extract the global features have achieved impressive results in the face clustering task. However, these works have a main drawback that they ignore the influence of the local features. In this paper, we propose a Context-Aware Graph Convolutional Network (CAGCN) to explicitly consider both the global and local information. We also propose a deduplication algorithm based on the Jaccard Similarity to improve the efficiency of face clustering. Experiments show that the proposed method can improve the integrity of the feature representations and the robustness of the clustering algorithm. We applied our algorithm on three popular large-scale benchmarks and achieved state-of-the-art performance comparing to the existing methods.