Lately there exist increasing demands for online abnormality monitoring over trajectory streams, which are obtained from moving object tracking devices. This problem is challenging due to the requirement of high speed data processing within limited space cost. In this paper, we present a novel framework for monitoring anomalies over continuous trajectory streams. First, we illustrate the importance of distance-based anomaly monitoring over moving object trajectories. Then, we utilize the local continuity characteristics of trajectories to build local clusters upon trajectory streams and monitor anomalies via efficient pruning strategies. Finally, we propose a piecewise metric index structure to reschedule the joining order of local clusters to further reduce the time cost. Our extensive experiments demonstrate the effectiveness and efficiency of our methods.