Recent years have witnessed the prevalence of networked data in various domains. Among them, a large number of networks are not only topologically structured but also have a rich set of features on nodes. These node features are usually of high dimensionality with noisy, irrelevant and redundant information, which may impede the performance of other learning tasks. Feature selection is useful to alleviate these critical issues. Nonetheless, a vast majority of existing feature selection algorithms are predominantly designed in a static setting. In reality, real-world networks are naturally dynamic, characterized by both topology and content changes. It is desirable to capture these changes to find relevant features tightly hinged with network structure continuously, which is of fundamental importance for many applications such as disaster relief and viral marketing. In this paper, we study a novel problem of time-evolving feature selection for dynamic networks in an unsupervised scenario. Specifically, we propose a TeFS framework by leveraging the temporal evolution property of dynamic networks to update the feature selection results incrementally. Experimental results show the superiority of TeFS over the state-of-The-Art batch-mode unsupervised feature selection algorithms.