In this paper, we tackle the task of online video temporal grounding (OnVTG), which requires the model to locate events related to a given natural language query within a video stream. Unlike regular video temporal grounding, OnVTG requires the model to make predictions without observing future frames. As online videos are streaming inputs and can go on indefinitely, it is impractical and inefficient to store all historical inputs. The existing OnVTG model employs memory to store recent historical video frame features and predict scores indicating whether the current frame corresponds to the start or end time of the target event. However, these methods lack effective event modeling and cannot retain long-term historical information, leading to low performance. To tackle these challenges, we propose hierarchical event memory for online video temporal grounding. We propose an event-based OnVTG framework that makes predictions based on event proposals that model event-level information with various durations. To efficiently preserve historically valuable event information, we introduce a hierarchical event memory that retains long-term low-redundant historical events, allowing the model to access both recent fine-grained information and long-term coarse-grained information. To enable the real-time prediction of the start time, we further propose a future prediction branch that predicts whether the target event will occur in the near future and further regress the start time of the event. By combining these two methods, we achieve efficient, accurate, and real-time online video temporal localization. We validate the effectiveness of our method on the ActivityNet Captions, TACoS, and MAD datasets.