Modeling relation between actors is important for recognizing group activity in a multi-person scene. This paper aims at learning discriminative relation between actors efficiently using deep models. To this end, we propose to build a flexible and efficient Actor Relation Graph (ARG) to simultaneously capture the appearance and position relation between actors. Thanks to the Graph Convolutional Network, the connections in ARG could be automatically learned from group activity videos in an end-to-end manner, and the inference on ARG could be efficiently performed with standard matrix operations. Furthermore, in practice, we come up with two variants to sparsify ARG for more effective modeling in videos: spatially localized ARG and temporal randomized ARG. We perform extensive experiments on two standard group activity recognition datasets: the Volleyball dataset and the Collective Activity dataset, where state-of-the-art performance is achieved on both datasets. We also visualize the learned actor graphs and relation features, which demonstrate that the proposed ARG is able to capture the discriminative relation information for group activity recognition.