Dynamic networks are a general language for describing time-evolving complex systems, and discrete time network models provide an emerging statistical technique for various applications. It is a fundamental research question to detect the community structure in time-evolving networks. However, due to significant computational challenges and difficulties in modeling communities of time-evolving networks, there is little progress in the current literature to effectively find communities in time-evolving networks. In this work, we propose a novel model-based clustering framework for time-evolving networks based on discrete time exponential-family random graph models. To choose the number of communities, we use conditional likelihood to construct an effective model selection criterion. Furthermore, we propose an efficient variational expectation-maximization (EM) algorithm to find approximate maximum likelihood estimates of network parameters and mixing proportions. By using variational methods and minorization-maximization (MM) techniques, our method has appealing scalability for large-scale time-evolving networks. The power of our method is demonstrated in simulation studies and empirical applications to international trade networks and the collaboration networks of a large American research university.