Abstract Timeline summarization targets at concisely summarizing the evolution trajectory along the timeline and existing timeline summarization approaches are all based on extractive methods. In this paper, we propose the task of abstractive timeline summarization, which tends to concisely paraphrase the information in the time-stamped events. Unlike traditional document summarization, timeline summarization needs to model the time series information of the input events and summarize important events in chronological order. To tackle this challenge, we propose a memory-based timeline summarization model (MTS). Concretely, we propose a time-event memory to establish a timeline, and use the time position of events on this timeline to guide generation process. Besides, in each decoding step, we incorporate event-level information into wordlevel attention to avoid confusion between events. Extensive experiments are conducted on a largescale real-world dataset, and the results show that MTS achieves the state-of-the-art performance in terms of both automatic and human evaluations