One of the most interesting application scenarios in anomaly detection is when sequential data are targeted. For example, in a safety-critical environment, it is crucial to have an automatic detection system to screen the streaming data gathered by monitoring sensors and to report abnormal observations if detected in real-time. Oftentimes, stakes are much higher when these potential anomalies are intentional or goal-oriented. We propose an end-to-end framework for sequential anomaly detection using inverse reinforcement learning (IRL), whose objective is to determine the decision-making agent's underlying function which triggers his/her behavior. The proposed method takes the sequence of actions of a target agent (and possibly other meta information) as input. The agent's normal behavior is then understood by the reward function which is inferred via IRL. We use a neural network to represent a reward function. Using a learned reward function, we evaluate whether a new observation from the target agent follows a normal pattern. In order to construct a reliable anomaly detection method and take into consideration the confidence of the predicted anomaly score, we adopt a Bayesian approach for IRL. The empirical study on publicly available real-world data shows that our proposed method is effective in identifying anomalies.