A control apparatus of a gas turbine system which includes a compressor configured to produce compressed air by sucking and compressing external air, a combustor configured to produce high-temperature high-pressure combustion gas by combusting the compressed air and fuel, and a turbine including a rotor rotated by the combustion gas produced through the combustor , wherein the compressor and the turbine are coaxially connected and a speed of the turbine rotor is proportional to a system frequency, the control apparatus comprising: a sensing unit configured to measure the turbine rotor speed; a compressed air amount estimation unit configured to estimate a change rate M R of an amount of compressed air which is produced by the compressor and supplied to the combustor , based on the measured turbine rotor speed; and a fuel amount control unit the control apparatus being characterised in 1 that the fuel amount control unit is configured to control a fuel amount F C supplied to the combustor , based on the estimated change rate M R , wherein the change rate M R of the compressed air amount is estimated according to M R = N C N N − 1 , where N C denotes the measured turbine rotor speed, and N N denotes the turbine rotor speed when the system frequency is a rated frequency; wherein the sensing unit is further configured to measure the amount of compressed air which is produced by the compressor and supplied to the combustor , wherein the compressed air amount is measured using at least one parameter of an inlet temperature of the compressor , a position of an inlet guide vane for inducing air to the compressor , and the turbine rotor speed; and wherein the compressed air amount estimation unit is further configured to correct the estimated change rate M R , based on the measured compressed air amount and wherein the compressed air amount estimation unit is further configured to store the compressed air amount in a database and to correct the estimated change rate M R , based on data stored in the database. a sensing unit configured to measure the turbine rotor speed; a compressed air amount estimation unit configured to estimate a change rate M R of an amount of compressed air which is produced by the compressor and supplied to the combustor , based on the measured turbine rotor speed; and a fuel amount control unit the control apparatus being characterised in 1 that the fuel amount control unit is configured to control a fuel amount F C supplied to the combustor , based on the estimated change rate M R , wherein the change rate M R of the compressed air amount is estimated according to M R = N C N N − 1 , where N C denotes the measured turbine rotor speed, and N N denotes the turbine rotor speed when the system frequency is a rated frequency; wherein the sensing unit is further configured to measure the amount of compressed air which is produced by the compressor and supplied to the combustor , wherein the compressed air amount is measured using at least one parameter of an inlet temperature of the compressor , a position of an inlet guide vane for inducing air to the compressor , and the turbine rotor speed; and wherein the compressed air amount estimation unit is further configured to correct the estimated change rate M R , based on the measured compressed air amount and wherein the compressed air amount estimation unit is further configured to store the compressed air amount in a database and to correct the estimated change rate M R , based on data stored in the database. <EOS>