With the increasing availability of modern mobile devices and location acquisition technologies, massive trajectory data of moving objects are collected continuously in a streaming manner. Clustering streaming trajectories facilitates finding the representative paths or common moving trends shared by different objects in real time. Although data stream clustering has been studied extensively in the past decade, little effort has been devoted to dealing with streaming trajectories. The main challenge lies in the strict space and time complexities of processing the continuously arriving trajectory data, combined with the difficulty of concept drift. To address this issue, we present two novel synopsis structures to extract the clustering characteristics of trajectories, and develop an incremental algorithm for the online clustering of streaming trajectories (called OCluST). It contains a micro-clustering component to cluster and summarize the most recent sets of trajectory line segments at each time instant, and a macro-clustering component to build large macro-clusters based on micro-clusters over a specified time horizon. Finally, we conduct extensive experiments on four real data sets to evaluate the effectiveness and efficiency of OCluST, and compare it with other congeneric algorithms. Experimental results show that OCluST can achieve superior peformance in clustering streaming trajectories.