In this study, we developed a diagnosis method for combustion instability and validated its performance using experimental data obtained from a hydrogen/natural gas co-firing gas turbine combustor. Four criteria, namely temporal kurtosis, permutation entropy, energy entropy, and zero-crossing rate, were considered. First, the performance of each criterion was compared with that of the conventional method for determining combustion instability using the root mean square (RMS) of dynamic pressure. Temporal kurtosis the best performance in terms of detection speed (instability onset detected 0.71 s earlier than the RMS method). Permutation entropy yielded the best performance in terms of accuracy and precision with accuracy, recall, precision, and F1-score values of 96.6%, 100%, 92.6%, and 96.2%, respectively. The performances of combinations of these criteria were investigated using AND and OR gates. Twenty-two cases were considered and the combination of permutation entropy and zero-crossing rate (best case) achieved detection time, accuracy, precision, recall, and F1-score values of 8.49 s, 97.2%, 93.9%, 100%, and 96.8%, respectively. Other combinations exhibited competitive performance; however, the method combining two criteria was selected to simplify the computing process. The proposed method is expected to contribute to the safe and stable operation of hydrogen/natural gas co-firing gas turbines.