Recently, an abundant amount of urban vehicle trajectory data has been collected in road networks. Many studies have used machine learning algorithms to analyze patterns in vehicle trajectories to predict location sequences of individual travelers. Unlike the previous studies that used a discriminative modeling approach, this research suggests a generative modeling approach to learn the underlying distributions of urban vehicle trajectory data. A generative model for urban vehicle trajectories can better generalize from training data by learning the underlying distribution of the training data and, thus, produce synthetic vehicle trajectories similar to real vehicle trajectories with limited observations. Synthetic trajectories can provide solutions to data sparsity or data privacy issues in using location data. This research proposes TrajGAIL, a generative adversarial imitation learning framework for the urban vehicle trajectory generation. In TrajGAIL, learning location sequences in observed trajectories is formulated as an imitation learning problem in a partially observable Markov decision process. The model is trained by the generative adversarial framework, which uses the reward function from the adversarial discriminator. The model is tested with both simulation and real-world datasets, and the results show that the proposed model obtained significant performance gains compared to existing models in sequence modeling.