There is known a technology in which in an arrangement where a catalyst is disposed in an exhaust passage of an internal combustion engine, when the internal combustion engine is driven in a fuel cut-off operation, an amount of gas (an amount of air) passing through the catalyst is made to increase, thereby suppressing an excessive rise in the temperature of the catalyst. In addition, there is also known a technology in which in the case where the fuel cut-off operation of the internal combustion engine is carried out, when the temperature of the catalyst is low, the amount of air passing through the catalyst is made to decrease, thereby suppressing excessive cooling of the catalyst (for example, see a first patent literature).