Group activity recognition can remarkably improve the understanding of video content by analyzing human behaviors and activities in videos. We propose a random walk graph convolutional network (RWGCN) for group activity recognition. (1) Considering the limitation of the convolutional structure to the visual information of group activities, the position feature extraction module is used to compensate for the loss of visual information. (2) A graph convolutional network (GCN) with distance-adaptive edge relations is constructed using individuals as graph nodes to identify the intrinsic relationships among the individuals in the group activities. (3) A Levy flight random walk mechanism is introduced into the GCN to obtain information from different nodes and integrate the previous position information to recognize group activity. Extensive experiments on the publicly available CAD, CAE datasets, and self-built BJUT-GAD dataset show that our RWGCN achieves MPCA of 95.49%, 94.82%, and 96.02%, respectively, which provides a better competitiveness in group activity recognition compared to other methods.