Traditional abnormal trajectory detection algorithms mainly involve the measurement of a single feature; however, the influence of other features on abnormal trajectory is ignored, resulting in the inability to fully discover the abnormal trajectory in the trajectory database. To overcome this limitation, we propose an abnormal trajectory detection method-called TADSS-to find the hidden abnormal trajectory by using a comprehensive measurement. Firstly, we employ three kernel functions to measure the time, velocity and position feature values of trajectory data, where the kernel functions extract semantic feature of the position, time feature of trajectory, and velocity feature of object motion from each trajectory data. Secondly, we propose a feature fusion strategy to measure the similarity of trajectory data, where we assign weights to the above kernel functions and then use a linear combination approach to fuse the weighted kernel functions. Thirdly, we build a trajectory feature graph by using the above fused kernel functions, and then divide the trajectory feature graph into a plurality of subgraphs by using a conventional graph clustering technique. Last, we propose a sparse subgraph method to detect abnormal trajectory, where a novel weight coefficient concept is used to distinguish sparse subgraph. Experimental results driven by both the vehicle trajectory data of Shanghai city and the Atlantic hurricane data demonstrate the performance of our TADSS.