Trip recommender system, which targets at recommending a trip consisting of several ordered Points of Interest (POIs), has long been treated as an important application for many location-based services. Currently, most prior arts generate trips following pre-defined objectives based on constraint programming, which may fail to reflect the complex latent patterns hidden in the human mobility data. And most of these methods are usually difficult to respond in real time when the number of POIs is large. To that end, we propose an Adversarial Neural Trip Recommendation (ANT) framework to tackle the above challenges. First of all, we devise a novel attention-based encoder-decoder trip generator that can learn the correlations among POIs and generate well-designed trips under given constraints. Another novelty of ANT relies on an adversarial learning strategy integrating with reinforcement learning to guide the trip generator to produce high-quality trips. For this purpose, we introduce a discriminator, which distinguishes the generated trips from real-life trips taken by users, to provide reward signals to optimize the generator. Moreover, we devise a novel pre-train schema based on learning from demonstration, which speeds up the convergence to achieve a sufficient-and-efficient training process. Extensive experiments on four real-world datasets validate the effectiveness and efficiency of our proposed ANT framework, which demonstrates that ANT could remarkably outperform the state-of-the-art baselines with short response time.