Human action recognition is one of the challenging and active research fields due to its wide applications. Recently, graph convolutions for skeleton-based action recognition have attracted much attention. Generally, the adjacency matrices of the graph are fixed to the hand-crafted physical connectivity of the human joints, or learned adaptively via deep learining. The hand-crafted or learned adjacency matrices are fixed when processing each frame of an action sequence. However, the interactions of different subsets of joints may play a core role at different phases of an action. Therefore, it is reasonable to evolve the graph topology with time. In this paper, a recurrent graph convolution is proposed, in which the graph topology is evolved via a long short-term memory (LSTM) network. The proposed recurrent graph convolutional network (R-GCN) can recurrently learn the data-dependent graph topologies for different layers, different time steps and different kinds of actions. Experimental results on the NTU RGB+D and Kinetics-Skeleton datasets demonstrate the advantages of the proposed R-GCN.