A control apparatus for an internal combustion engine is provided. The control apparatus is equipped with an electronic control unit. A CPU with which this electronic control unit is equipped performs dither control for setting a first cylinder as a rich-burn cylinder whose air-fuel ratio is richer than a theoretical air-fuel ratio and setting each of second to fourth cylinders as a lean-burn cylinder whose air-fuel ratio is leaner than the theoretical air-fuel ratio, when a request to raise the temperature of a three-way catalyst is made. Then, the CPU reduces the degree of richness of the rich-burn cylinder and the degree of leanness of each of the lean-burn cylinders while continuing dither control, on the condition that fluctuations at a level equal to or higher than a predetermined value are caused in time-series data on the rotational speed resulting from the combustion in each of the cylinders.