A gas turbine combustion instability control device has a combustion unit provided with a hollow combustion chamber, a gas turbine connected to the inside of the combustion chamber and a dynamic pressure sensor which is provided to the inside of the combustion chamber and measures the combustion dynamics of the inside of the combustion chamber; a diagnosis module which processes combustion dynamic pressure signals (p) according to the combustion dynamics measured by the dynamic pressure sensor to calculate the kurtosis value (k) of the dynamic pressure signals, and compares the same with a kurtosis reference value (kth) to evaluate the combustion instability; and a combustion control unit for controlling the operation of the combustion part according to the determination of the diagnosis module.