Social networks are large systems that depict linkage between millions of social entities. The study of their patterning and evolving is one of the major research areas in social network analysis and network mining. It includes the prediction of future associations between unlinked nodes, known as the link prediction problem. Traditional methods are designed to deal with social networks under a certain framework. Yet, data of such networks are usually noisy, missing and prone to observation errors causing distortions and likely inaccurate results. This paper addresses the link prediction problem under the uncertain framework of the belief function theory, an appealing framework for reasoning under uncertainty that permits to represent, quantify and manage imperfect evidence. Firstly, a new graph based model for social networks that handles uncertainties in links' structures is introduced. Secondly, a novel method for the prediction of new links that makes use of the belief functions tools is proposed. It takes advantage of both neighborhood and common groups information in social networks in order to predict new connections. The performance of the new method is validated on real world social networks. Experiments show that our approach performs better than traditional methods based on structural information.