Modeling the evolution of user preference is essential in recommender systems. Recently, dynamic graph-based methods have been studied and achieved SOTA for recommendation, majority of which focus on user's stable long-term preference. However, in real-world scenario, user's short-term preference evolves over time dynamically. Although there exists sequential methods that attempt to capture it, how to model the evolution of short-term preference with dynamic graph-based methods has not been well-addressed yet. In particular: 1) existing methods do not explicitly encode and capture the evolution of short-term preference as sequential methods do; 2) simply using last few interactions is not enough for modeling the changing trend. In this paper, we propose Long Short-Term Preference Modeling for Continuous-Time Sequential Recommendation (LSTSR) to capture the evolution of short-term preference under dynamic graph. Specifically, we explicitly encode short-term preference and optimize it via memory mechanism, which has three key operations: Message, Aggregate and Update. Our memory mechanism can not only store one-hop information, but also trigger with new interactions online. Extensive experiments conducted on five public datasets show that LSTSR consistently outperforms many state-of-the-art recommendation methods across various lines.