PURPOSE: To prevent fuel cut deviating to one of first and second cylinder groups divided, by controlling to alternately conduct the fuel cut in the first cylinder group and the second cylinder group according to an excessive quantity over a predetermined fuel cut engine speed.

CONSTITUTION: Operational condition detecting means a is provided to detect an engine operational condition according to an engine load and an engine speed as parameters. Excessive quantity computing means b is provided to compare the engine speed with a predetermined fuel cut engine speed and compute an excessive quantity over the predetermined fuel cut engine speed. Fuel cut execution mode setting means c is provided to divide cylinders into two groups for executing the fuel cut and set a fuel cut execution mode such that the two cylinder groups alternately execute the fuel cut according to the excessive quantity. When the engine speed exceeds the predetermined fuel cut engine speed, cut commanding means d designates the cylinder group for executing the fuel cut, and a fuel supply quantity is corrected per cylinder group by fuel supply quantity computing means e.