Link prediction aims to uncover the underlying relationship behind networks, which could be utilized to predict the missing edges or identify the spurious edges, and attracts much attention from various fields. The key issue of link prediction is to estimate the likelihood of two nodes in networks. Most current approaches of link prediction base on static structural analysis and ignore the temporal aspects of evolving networks. Unlike previous work, in this paper, we propose a popularity based structural perturbation method (PBSPM) that characterizes the similarity of an edge not only from existing connections of networks, but also from the popularity of its two endpoints, since popular nodes have much more probability to form links between themselves. By taking popularity of nodes into account, PBSPM could suppress nodes that have high importance, but gradually become inactive. Therefore the proposed method is inclined to predict potential edges between active nodes, rather than edges between inactive nodes. Experimental results on four real networks show that the proposed method outperforms the state-of-the-art methods both in accuracy and robustness in evolving networks.