An apparatus for controlling the air-fuel ratio of an internal combustion engine to stably determine a highly reliable identified value of a parameter of a model of an exhaust system including a catalytic converter and to increase the purifying capability of the catalytic converter. An exhaust-side control unit 7a sequentially variably sets a dead time of an exhaust system E depending on the flow rate of an exhaust gas supplied to a catalytic converter 3, and sequentially identifies the value of a parameter of a model of the exhaust system E which has a dead time element of the set dead time. The exhaust-side control unit 7a sequentially calculates a target air-fuel ratio KCMD to converge the output of an O.sub.2 sensor 6 to a target value using the identified value of the parameter, and an engine-side control unit 7b manipulates the air-fuel ratio of the internal combustion engine 1 depending on the target air-fuel ratio KCMD. According to the algorithm of the process of identifying the parameter of the model of the exhaust system E, the value of a weighted parameter is variable set depending on the flow rate of the exhaust gas.