Trending topics in social media content evolve over time, and it is therefore crucial to understand social media users and their interpersonal communications in a dynamic manner. Here we study dynamic online conversation recommendation, to help users engage in conversations that satisfy their evolving interests. While most prior work assumes static user interests, our model is able to capture the temporal aspects of user interests, and further handle future conversations that are unseen during training time. Concretely, we propose a neural architecture to exploit changes of user interactions and interests over time, to predict which discussions they are likely to enter. We conduct experiments on large-scale collections of Reddit conversations, and results on three subreddits show that our model significantly outperforms state-of-the-art models that make a static assumption of user interests. We further evaluate on handling “cold start”, and observe consistently better performance by our model when considering various degrees of sparsity of user’s chatting history and conversation contexts. Lastly, analyses on our model outputs indicate user interest change, explaining the advantage and efficacy of our approach.