Due to the fact that the combustion system, the core component of gas turbines, works in the highly adverse environmental conditions of high temperature and high pressure, it frequently faces malfunctions, causing catastrophic accidents. Hence, anomaly detection plays an important role in helping the combustion system run safely and economically. In recent decades, some methods have been published on anomaly detection of the gas turbine combustion system. However, there are few studies that compare these methods. The aim of this paper is to review and provide analytical results of the anomaly detection methods. An overall assessment of the merits or weaknesses of the generic methods is provided by testing the methods with actual gas turbine operating data. Additionally, some possible research development of the anomaly detection of the gas turbine combustion system is presented in this comparative study.