Argument structure extraction is a fundamental problem in argumentation mining which aims at automatically constructing arguments from unstructured textual documents. Re-garding each argument as a node, then predicting relationships of those nodes is a key task for argument structure extraction, which is called link prediction. Graph neural networks (GNN), as an efficient approach to cope with graphical data, have shown good performances on link prediction tasks. However, they usually focus on predicting whether parts of links really exist in one argument graph, rather than predicting existence of the links between any two nodes, though it is more practical in real applications of argument mining. Thus, in this paper our goal is to predict links between any two nodes given only nodes information. This task is more difficult than the traditional link prediction tasks since the prediction scale exponentially increases with node number. We propose a GNN based model for link predic-tion which outputs the embedding of all the nodes. Then, the probability of link existence between any two nodes is calculated by their embedding results. Finally, we use a dataset of essay comments to perform evaluations and the results confirm the effectiveness of our proposed method.