PURPOSE: To improve engine durability, by continuously changing an cylinder to be stopped for uniforming the temperature in the inside of an internal combustion engine in cylinder cut-off operation.

CONSTITUTION: In a cut-off cylinder calculating means the number of cylinders, for which fuel supply is to be stopped, is calculated based on the slip ratio of a driving wheel, calculated by a slip ratio calculating means, and the operation condition of an internal combustion engine, calculated by an operation condition detecting means. By an output torque control means, fuel supply stop control is performed according to the calculated result of a calculating means for the number of cylinders to be stopped and by changing in order a cylinder for stopping fuel supply. In a fuel quantity increase control means, fuel supply quantity to an internal combustion engine is controlled so as to supply fuel, to which a given increased quantity value is added, to only a cylinder returned to an operating condition from a fuel supply stop condition. At that time by an increased-quantity change control means, an increased-quantity value to be added, according to the number of cylinders to be stopped calculated by the calculating means for the number of cylinders to be stopped, is changed. Consequently, temperature distribution for all cylinders can be nearly made uniform to improve the durability of an internal combustion engine.