In an apparatus for controlling a general-purpose engine used as a prime mover of an operating machine, the apparatus regulating a throttle opening such that an engine speed is converged to a desired engine speed, calculating a basic fuel injection amount based on the engine speed and throttle opening, and controlling engine warm-up operation by correcting the basic fuel injection amount with a correction coefficient to calculate a warm-up time fuel injection amount after engine start is completed and injecting fuel by the calculated amount, a fuel injection amount with which the engine output becomes maximum is searched based on the throttle opening regulated in response to increase/decrease operation of the warm-up time fuel injection amount conducted when the engine speed is constant; and the correction coefficient is corrected using the searched fuel injection amount. With this, a warm-up correction coefficient appropriate for the engine warm-up condition can be calculated.