Mobile computing is a new technology emerging with the development of mobile communication, Internet, database, distributed computing, and other technologies. Mobile computing technology will enable computers or other information intelligent terminal devices to realize data transmission and resource sharing in the wireless environment. Its role is to bring useful, accurate, and timely information to any customer at anytime, anywhere, and to change the way people live and work. In mobile computing environment, a lot of Internet rumors hidden among the huge amounts of information communication network can cause harm to society and people’s life; this paper proposes a model of social network rumor detection based on convolution networks, the use of adjacency matrix between the nodes represent user and the relationship between the constructions of social network topology. We use a high-order graph neural network (K-GNN) to extract the rumor posting features. At the same time, the graph attention network (GAT) is used to extract the association features of other nodes of the network topology. The experimental results show that the method of the detection model in this paper improves the accuracy of prediction classification compared with deep learning methods such as RNN, GRU, and attention mechanism. The innovation of the paper proposes a rumor detection model based on the graph convolutional network, which lies in considering the propagation structure among users. It has a strong practical value.