Link prediction plays an important role in understanding the intrinsic evolving mechanisms of networks. With the belief that the likelihood of the existence of a link between two nodes is strongly related to their similarity, many methods have been proposed to calculate node similarity based on node attributes and/or topological structures. Among a large variety of methods that take into account paths connecting the target pair of nodes, most of them neglect the heterogeneity of those paths. Our hypothesis is that a path consisting of small-degree nodes provides a strong evidence of similarity between two ends, accordingly, we propose a so-called significant path index in this letter to leverage intermediate nodes' degrees in similarity calculation. Empirical experiments on twelve disparate real networks demonstrate that the proposed index outperforms the mainstream link prediction baselines.