Link prediction is defined as the prediction of potential relationships between nodes in the future based on the known network topology and the node information. Link prediction can help reduce resource expenditure and allocate resources more reasonably in various applications including links. Mobile social network is a kind of dynamic network, and its structure is always evolving with the appearance and disappearance of nodes and links over time. According to the characteristics of the mobile social network, the current existing researches use more sophisticated model to analyze the relationship between the links, however complex models not only have large space complexity but also are easy to over fitting problem. In order to solve the above problems, a gating cycle unit based on the prediction method of mobile social network link is put forward. Firstly, the input data set is sorted and filtered, and the target network is divided into snapshot graphs and transformed into adjacency matrices to form a sample set. Then, the prediction model is constructed based on the auto encoder and the gated recurrent units to extract the temporal characteristics of mobile social network. Based on KONECT dataset, the experimental results compared with other models show that the proposed method can improve the training efficiency by 49.81%, while the prediction performance can be maintained.