With the increasing popularity of the social network Twitter and its use to propagate information, it is of vital importance to detect rumors prior to their dissemination on Twitter. In the present paper, a model to detect rumor conversations is proposed using graph convolutional networks. A reply tree and user graph were extracted for each conversation. The reply trees were created according to the source tweet and the reply tweets. By modeling this graph on graph convolutional networks, structural information of the graph and the contents of conversation tweets were obtained. The user graphs were created based on the users participating in the conversation and the tweets exchanged among them. Information regarding the users and how they interacted in the conversations were obtained through modeling this graph on the graph convolutional networks. The outputs of the two above-mentioned modules were combined to detect the rumor. Experimental results on the public dataset show that the proposed method has a better performance than baseline methods.