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.