Link prediction is an important issue in graph data mining. In social networks, link prediction is used to predict missing links in current networks and new links in future networks. This process has a wide range of applications including recommender systems, spam mail classification, and the identification of domain experts in various research areas. In order to predict future node similarity, we propose a new model, Common Influence Set, to calculate node similarities. The proposed link prediction algorithm uses the common influence set of two unconnected nodes to calculate a similarity score between the two nodes. We used the area under the ROC curve (AUC) to evaluate the performance of our algorithm and that of previous link prediction algorithms based on similarity over a range of problems. Our experimental results show that our algorithm outperforms previous algorithms.