The increasing availability of large-scale location traces creates unprecedent opportunities to change the paradigm for identifying abnormal moving activities. Indeed, various aspects of abnormality of moving patterns have recently been exploited, such as wrong direction and wandering. However, there is no recognized way of combining different aspects into an unified evolving abnormality score which has the ability to capture the evolving nature of abnormal moving trajectories. To that end, in this paper, we provide an evolving trajectory outlier detection method, named TOP-EYE, which continuously computes the outlying score for each trajectory in an accumulating way. Specifically, in TOP-EYE, we introduce a decay function to mitigate the influence of the past trajectories on the evolving outlying score, which is defined based on the evolving moving direction and density of trajectories. This decay function enables the evolving computation of accumulated outlying scores along the trajectories. An advantage of TOP-EYE is to identify evolving outliers at very early stage with relatively low false alarm rate. Finally, experimental results on real-world location traces show that TOP-EYE can effectively capture evolving abnormal trajectories.