The opening of a solenoid valve is automatically adjusted after an engine is started and before actual work is performed for an appropriate air-fuel ratio, whereby it is possible to attain a good and stable driving of the engine without any delay even for an abrupt change in load. After the engine is started, when a rotation speed enters a “fuel flow rate adjusting rotation speed range” in which a definite load is applied to the engine in a working rotation speed range of the engine in which a throttle valve is opened to a definite opening, a detected rotation speed is fed back to a target rotation speed, and the opening of the solenoid valve is controlled to adjust a fuel flow rate, so that the combustion state in the engine is optimized at the valve opening so determined.