Link prediction, aiming to find missing links in an observed network or predict those links that may occur in the future, has become a basic challenge of network science. Most existing link prediction methods are based on local or global topological attributes of the network such as degree, clustering coefficient, path index, etc. In the process of resource allocation, as the number of connections between the common neighbors of the paired nodes increases, it is easy to leak information through them. To overcome this problem, we proposed a new similarity index named ESHOPI (link prediction based on Dempster–Shafer theory and the importance of higher-order path index), which can prevent information leakage by penalizing ordinary neighbors and considering the information of the entire network and each node at the same time. In addition, high-order paths are used to improve the performance of link prediction by penalizing the longer reachable paths between the seed nodes. The effectiveness of ESHOPI is shown by the experiments on both synthetic and real-world networks.