Detecting anomalous trajectory has become an im- portant and fundamental concern in many real-world applica- tions. However, most of the existing studies 1) cannot handle the complexity and variety of trajectory data and 2) do not support efficient anomaly detection in an online manner. To this end, we propose a novel model, namely Gaussian Mixture Variational Sequence AutoEncoder (GM-VSAE), to tackle these challenges. Our GM-VSAE model is able to (1) capture complex sequential information enclosed in trajectories, (2) discover different types of normal routes from trajectories and represent them in a continuous latent space, and (3) support efficient online detection via trajectory generation. Our experiments on two real-world datasets demonstrate that GM-VSAE is more effective than the state-of-the-art baselines and is efficient for online anomalous trajectory detection.