Given the explosive growth of large-scale services, manually detecting problems from console logs is infeasible. In the current study, we propose a novel process mining algorithm to discover process model from console logs, and further use the obtained process model to detect anomalies. In brief, the console logs are first parsed into events, and the events from one single session are further grouped to event sequences. Then, a process model is mined from the event sequences to describe the main system behaviors. At last, we use the process model to detect anomalous log information. Experiments on Hadoop File System log dataset show that this approach can detect anomalies from log messages with high accuracy and few false positives. Compared with previously proposed automatic anomaly detection methods, our approach can provide intuitive and meaningful explanations to human operators as well as identify real problems accurately. Furthermore, the process model is easy to understand.