An air-fuel ratio control apparatus of an internal combustion engine in which an exhaust gas purifying catalyst is disposed in an exhaust passage, comprises: fuel cut means which stops fuel supply to the internal combustion engine when it is determined that a number of revolutions of the internal combustion engine is higher than a fuel cut number of revolutions at the time of deceleration of the internal combustion engine; and changing means of the fuel cut number of revolutions for changing the fuel cut number of revolutions according to a physical amount which correlates with an amount of oxygen discharged from the exhaust gas purifying catalyst during the fuel increasing operation of the internal combustion engine such that as the amount of oxygen is greater, the fuel cut number of revolutions is reduced.