1. An air-fuel ratio control apparatus of an internal combustion engine, comprising: a fuel injection valve driven based on an injection signal input thereto to inject fuel; an air-fuel ratio sensor detecting an actual air-fuel ratio; and a control unit calculating a fuel injection quantity using a feedback control amount based on said actual air-fuel ratio and a target air-fuel ratio, to output an injection signal corresponding to said fuel injection quantity to said fuel injection valve, wherein said control unit: sequentially identifies a plant model representing a plant between said fuel injection valve and said air-fuel ratio sensor, to calculate an input side parameter and output side parameters set, respectively, on an input side and an output side of said plant model; calculates a control gain for calculating said feedback control amount using the calculated input side parameter and output side parameters, when an absolute value of the calculated input side parameter is a predetermined limit value or above; calculates said control gain using said limit value and the calculated output side parameters, when the absolute value of the calculated input side parameter is less than said limit value; and calculates said feedback control amount using the calculated control gain.