Internal combustion engine air-fuel ratio control apparatus and method in which the target air-fuel ratio of exhaust gas flowing into an exhaust-gas purification catalyst unit is controlled through at least proportional-integral control such that the correction amount per unit time of the oxygen amount in said catalyst unit is maintained constant. When the intake air amount is smaller than a predetermined amount and the air-fuel ratio detected by an oxygen sensor provided downstream of the catalyst unit is rich, the target air-fuel ratio is controlled to suppress an increase in the air-fuel ratio in the exhaust-gas purification catalyst unit. Accordingly, even if rapid acceleration operation is performed in a state where the intake air amount is extremely small and the air-fuel ratio detected by the oxygen sensor is rich, NOx in exhaust gas can be sufficiently removed through reduction reactions at the exhaust-gas purification catalyst unit.