Abstract Modeling trajectory data is a building block for many smart-mobility initiatives. Existing approaches apply shallow models such as Markov chain and inverse reinforcement learning to model trajectories, which cannot capture the long-term dependencies. On the other hand, deep models such as Recurrent Neural Network (RNN) have demonstrated their strength of modeling variable length sequences. However, directly adopting RNN to model trajectories is not appropriate because of the unique topological constraints faced by trajectories. Motivated by these ?ndings, we design two RNNbased models which can make full advantage of the strength of RNN to capture variable length sequence and meanwhile to address the constraints of topological structure on trajectory modeling. Our experimental study based on real taxi trajectory datasets shows that both of our approaches largely outperform the existing approaches.