A link prediction model for weighted networks based on Dempster–Shafer (DS) evidence theory and the influence of common neighbours is proposed in this paper. First, three types of future common neighbours (FCNs) and their topological structures are proposed. Second, the concepts of endpoint weight influence, link weight influence, and high-strength node influence are introduced. Then, the similarity based on the impacts of current common neighbours (CCNs) and FCNs is defined, respectively. Finally, the two similarity indices are fused by the DS evidence theory. This model effectively integrates multisource information and completely exploits the influence of all CCNs and FCNs on similarity. Experiments are performed on 9 real and 40 simulation-weighted datasets, and these findings are compared with several classic algorithms. Results show that the proposed method has higher precision than other methods, which can achieve good performance in link prediction in weighted networks.