Outlier detection has been a popular data mining task. However, there is a lack of serious study on outlier detection for trajectory data. Even worse, an existing trajectory outlier detection algorithm has limited capability to detect outlying sub-trajectories. In this paper, we propose a novel partition-and-detect framework for trajectory outlier detection, which partitions a trajectory into a set of line segments, and then, detects outlying line segments for trajectory outliers. The primary advantage of this framework is to detect outlying sub-trajectories from a trajectory database. Based on this partition-and-detect framework, we develop a trajectory outlier detection algorithm TRAOD. Our algorithm consists of two phases: partitioning and detection. For the first phase, we propose a two-level trajectory partitioning strategy that ensures both high quality and high efficiency. For the second phase, we present a hybrid of the distance-based and density-based approaches. Experimental results demonstrate that TRAOD correctly detects outlying sub-trajectories from real trajectory data.