PURPOSE: To prevent an air-fuel ratio from going to the rich side as well as to improve a rate of fuel consumption, by letting a controller perform on-off control over a slow cut valve at a time when air-fuel ratio compensation value is approximated to a range of 100% and simultaneously engine speed and throttle opening both become more than the specified value.

CONSTITUTION: At a control part 14 which controls the valve 16 installed in a carburetor for its opening or closing and also controls an air-fuel ratio for feedback, at the time of feedback control over the air-fuel ratio by an oxygen sensor 18, air-fuel compensation value is made to go up and simultaneously engine speed and throttle valve opening both are made to go up. And, when the air-fuel ratio compensation value is approximated to a range of 100% and simultaneously the engine speed and the throttle valve opening both become more than the specified value, a slow-cut valve is controlled for opening or closing at every T second interval. And, when any one of the air-fuel ratio compensation value, the engine speed and the throttle valve opening becomes less than the setting value, it is constituted so as to stop on-off control over the said slow-cut valve.