The problem of top-k influence maximization is to find the set of k users in a social network that can maximize the spread of influence under certain influence propagation model. This paper studies the influence maximization problem together with network dynamics. For example, given a real-life social network that evolves over time, we want to find k most influential users on everyday basis. This dynamic influence maximization problem has wide applications in practice. However, to our best knowledge, there is little prior work that studies this problem. Applying existing influence maximization algorithms at every time step provides a straightforward solution to the dynamic top-k influence maximization problem. Such a solution is, however, inefficient as it completely ignores the smoothness of network change. By analyzing two real social networks, Brightkite and Gowalla, we observe that the top-k influential set, as well as its influence value, does not change dramatically over time. Hence, it is possible to find the new top-k influential set by updating the previous one. We propose an efficient incremental update framework that takes advantage of such smoothness of network change. The proposed method achieves the same approximation ratio of 1 − e as its state-of-the-art static counterparts. Our experiments show that the proposed method outperforms the straightforward solution by a wide margin.