Monitoring gas turbine combustors health, in particular, early detecting abnormal behaviors and incipient faults, is critical in ensuring gas turbines operating efficiently and in preventing costly unplanned maintenance. One popular means of detecting combustor abnormalities is through continuously monitoring exhaust gas temperature profiles. Over the years many anomaly detection technologies have been explored for detecting combustor faults, however, the performance (detection rate) of anomaly detection solutions fielded is still inadequate. Advanced technologies that can improve detection performance are in great need. Aiming for improving anomaly detection performance, in this paper we introduce recently-developed deep learning (DL) in machine learning into the combustors anomaly detection application. Specifically, we use deep learning to hierarchically learn features from the sensor measurements of exhaust gas temperatures. And we then use the learned features as the input to a neural network classifier for performing combustor anomaly detection. Since such deep learned features potentially better capture complex relations among all sensor measurements and the underlying combustor behavior than handcrafted features do, we expect the learned features can lead to a more accurate and robust anomaly detection. Using the data collected from a real-world gas turbine combustion system, we demonstrated that the proposed deep learning based anomaly detection significantly indeed improved combustor anomaly detection performance.